Chaos: An Interdisciplinary Journal of Nonlinear Science

In this article a mathematical treatment of Covid-19 as a stochastic process is discussed. The chance of extinction and the consequences of introducing new Covid-19 infectives into the population are evaluated by using certain approximate arguments. It is shown, in general terms, that the stochastic formulation of a recurrent epidemic like Covid-19 leads to the prediction of a permanent succession of undamped outbreaks of disease. It is also shown that one is able to derive certain useful conclusions about Covid-19 without consideration of immune individuals in a population.

House hunting of ant, such as Temnothorax albipennis, has been shown to be a distributed dynamical system. Such a system includes agent-based algorithm [1], with agents in different roles including nest exploration, nest assessment, quorum sensing, and brood item transportation. Such an algorithm, if used properly, can be applied on artificial intelligent system, like robotic swarms. Despite of its complexity, we are focusing on the quorum sensing mechanism, which is also observed in bacteria model. In bacterial model, multiple biochemical networks co-exist within each cell, including binding of autoinducer and cognate receptors, and phosphorylation-dephosphorylation cycle. In ant hunting, we also have ant commitment to the nest, mimicking binding between autoinducer and cognate receptors. We also have assessment ant specific to one nest and information exchange between two assessment ants corresponding to different nests, which is similar process to the phosphorylation-dephosphorylation cycle in bacteria quorum sensing network. Due to the similarity between the two models, we borrow the idea from bacteria quorum sensing to clarify the definition of quorum threshold through biological plausible mechanism related to limited resource model. We further made use of the contraction analysis to explore the trade-off between decision split and decision consensus within ant population. Our work provides new generation model for understanding how ant adapt to the changing environment during quorum sensing.

The relationship between ratios of excitatory to inhibitory neurons and the brains dynamic range of cortical activity is crucial. However, its full understanding within the context of cortical scale-free dynamics remains an ongoing investigation. To provide insightful observations that can improve the current understanding of this impact, and based on studies indicating that a fully excitatory neural network can induce critical behavior under the influence of noise, it is essential to investigate the effects of varying inhibition within this network. Here, the impact of varying ratios on neural avalanches and phase transition diagrams, considering a range of control parameters in a leaky integrate-and-fire model network, is examined. Our computational results show that the network exhibits critical, sub-critical, and super-critical behavior across different control parameters. In particular, a certain ratio leads to a significantly extended dynamic range compared to others and increases the probability of the system being in the critical regime. To address differences between various ratios, we utilized the Kuramoto order parameter and conducted a finite-size scaling analysis to determine the critical exponents associated with phase transitions. In order to characterize the criticality, we examined the distribution of neuronal avalanches at the critical point and the scaling behavior characterized by specific exponents.

Inspired by heterogeneity in biological neural networks, we explore a heterogeneous network consisting of receipt, transmission and computation layers. It reconciles the dilemma that the data analysis scheme for empirical records yields non-power laws when applied to microscopic simulation of critical neural dynamics. Detailed analysis shows that the reconciliation is due to synchronization effect of the feedforward connectivity. The network favours avalanches with denser activity in the first half of life, and the result is consistent with the experimental observation. This heterogeneous structure facilitates robust criticality against external stimuli, which implies the inappropriateness of interpreting the subcritcality signature as an indication of subcrtical dynamics. These results propose the network heterogeneity as an essential piece for understanding the brain criticality.

Humans navigate diverse social relationships and concurrently interact across multiple social contexts. An individuals behavior in one context can influence behavior in other contexts. Different payoffs associated with interactions in the different domains have motivated recent studies of the evolution of cooperation through the analysis of multichannel games where each individual is simultaneously engaged in multiple repeated games. However, previous investigations have ignored the potential role of network structure in each domain and the effect of playing against distinct interacting partners in different domains. Multiplex networks provide a useful framework to represent social interactions between the same set of agents across different social contexts. We investigate the role of multiplex network structure and strategy linking in multichannel games on the spread of cooperative behavior in all layers of the multiplex. We find that multiplex structure along with strategy linking enhances the cooperation rate in all layers of the multiplex compared to a well-mixed population, provided the network structure is identical across layers. The effectiveness of strategy linking in enhancing cooperation depends on the degree of similarity of the network structure across the layers and perception errors due to imperfect memory. Higher cooperation rates are achieved when the degree of structural overlap of the different layers is sufficiently large, and the probability of perception error is relatively low. Our work reveals how the social network structure in different layers of a multiplex can affect the spread of cooperation by limiting the ability of individuals to link strategies across different social domains.

Collective responses to localized perturbations are essential for the adaptability of animal groups. Using a biologically grounded computational model of burst-and-coast swimming in Hemigrammus rhodostomus, we investigate how group size and the strength of social interactions shape collective dynamics under perturbation. The model integrates experimentally derived attraction and alignment rules, behavioral heterogeneity, and boundary effects within a circular tank. We identify four collective states (schooling, milling, turning, and swarming) and characterize a critical regime in which groups exhibit multistable dynamics. At this critical point, small subsets of perturbing individuals, defined by altered social interaction strengths, can induce sharp transitions to new collective states. In particular, such transitions occur in large groups (N = 100) but not in smaller ones (N = 25 or 50), highlighting a size-dependent sensitivity to disturbance. We show that both the nature of the perturbing individuals and the initial state of the group modulate the systems responsiveness. Our findings suggest that large groups may exploit criticality to remain both robust, flexible, and that individual variability can serve as a catalyst for adaptive reconfiguration. This work provides new insights into how the internal group structure and perturbation design influence collective behavior in animal groups.

The brain criticality hypothesis has been a central research topic in theoretical neuroscience for two decades. This hypothesis suggests that the brain operates near the critical point at the boundary between order and disorder, where it acquires its information-processing capabilities. The mechanism that maintains this critical state has been proposed as a feedback system known as self-organized criticality (SOC); brain parameters, such as synaptic plasticity, are regulated internally without external adjustment. Therefore, clarifying how SOC occurs can help us to understand the mechanisms that maintain brain function and cause brain disorders. From the standpoint of neural network structures, the topology of neural circuits also plays a crucial role in information processing, with healthy neural networks exhibiting small-world, scale-free, and modular characteristics. However, how these network structures affect SOC remains poorly understood. In this study, we numerically investigated the possibility that the structure of neural networks contributes to the brains critical state and dysfunction using a mathematical model. Our results reveal that the time scales at which synaptic plasticity operates to achieve a critical state differ depending on the network structure. Additionally, we observed Dragon king phenomena associated with abnormal neural activity, depending on the network structure and synaptic plasticity time scales. Notably, Dragon king was observed over a wide range of synaptic plasticity time scales in scale-free networks with high-degree hub nodes. This study emphasizes the importance of neural network topology in neuroscience from the perspective of SOC.

Signal transduction, underpinning the function of a variety of biological systems, is inevitably affected by fluctuations. It remains intriguing how the timescale of a signaling network relates to its capability of noise control, specifically, whether long timescale can average out fluctuation or accumulate fluctuation. Here, we consider two noise components of the signaling system: the upstream noise from the fluctuation of the input signal and the downstream noise from the stochastic fluctuations of the network. We discover a fundamental trade-off in controlling the upstream and downstream noise: a longer timescale of the signaling network can buffer upstream noise, while accumulate downstream noise. Moreover, we confirm that this trade-off relation exists in real biological signaling networks such as a fold-change detection circuit and the p53 activation signaling system. Author SummaryInformation transmission is vital in biological systems, such as decoding the information regarding nutrient levels during chemotaxis or morphogen concentrations in tissue development. While fluctuations arising from the stochastic nature of biological processes inevitably affect information transmission, noise control mechanisms have been studied for decades. However, it remains controversial what the role of the slow dynamics (long timescale) is in noise control. On the one hand, it has been reported to attenuate noise by averaging out fluctuations. On the other hand, it is also proposed to amplify noise by accumulating fluctuations. Here we dissect the noise in signaling systems into two components: upstream noise originating from signal fluctuation, and downstream noise from the network stochasticity. Our analysis reveals that upstream noise negatively correlates with timescale, while downstream noise exhibits a positive correlation, indicating a fundamental trade-off in controlling the two noise components. Moreover, we provide an intuitive illustration to understand this phenomenon using the concept of landscape representation. Mathematically, we analytically derive a trade-off relation that agrees well with simulations. Our results uncover a new property of noise in signaling processes, deepening our understanding of noise control and proposing a new perspective in designing signaling network.

Scale-free brain dynamics under external stimuli raises an apparent paradox since the critical point of the brain dynamics locates at the limit of zero external drive. Here, we demonstrate that relaxation of the membrane potential removes the critical point but facilitates scale-free dynamics in the presence of strong external stimuli. These findings feature biological neural networks as systems that have no real critical point but bear critical-like behaviors. Attainment of such pseudocritical states relies on processing neurons into a precritical state where they are made readily activatable. We discuss supportive signatures in existing experimental observations and advise new ones for these intriguing properties. These newly revealed repertoires of neural states call for reexamination of brains working states and open fresh avenues for the investigation of critical behaviors in complex dynamical systems.

Population is separated into five compartments for COVID-19; susceptible individuals (S), pre-symptomatic patients (P), asymptomatic patients (A), quarantined patients (Q) and recovered and/or dead patients (R). The time evolution of each compartment is described by a set of ordinary differential equations. Numerical solution to the set of differential equations shows that quarantining pre-symptomatic and asymptomatic patients is effective in controlling the pandemic. It is also shown that the ratio of non-symptomatic patients to the daily confirmed new cases can be as large as 20 and that the fraction of untraceable cases in new cases can be as large as 80%, depending on the policies for social distancing and PCR test.

Increasing number in global COVID-19 cases demands for mathematical model to analyze the interaction between the virus dynamics and the response of innate and adaptive immunity. Here, based on the assumption of a weak and delayed response of the innate and adaptive immunity in SARS-CoV-2 infection, we constructed a mathematical model to describe the dynamic processes of immune system. Integrating theoretical results with clinical COVID-19 patients data, we classified the COVID-19 development processes into three typical modes of immune responses, correlated with the clinical classification of mild & moderate, severe and critical patients. We found that the immune efficacy (the ability of host to clear virus and kill infected cells) and the lymphocyte supply (the abundance and pool of naive T and B cell) play important roles in the dynamic process and determine the clinical outcome, especially for the severe and critical patients. Furthermore, we put forward possible treatment strategies for the three typical modes of immune response. We hope our results can help to understand the dynamical mechanism of the immune response against SARS-CoV-2 infection, and to be useful for the treatment strategies and vaccine design.

Hidden collective organization of cancer cells can partially or completely return to embryoid genotype-phenotype with the plasticity to transform their morphology on cell embryoblast-like memory entities by expression of dormant genes that arise from embryogenesis. After hundreds of driver mutations, cancer cells gain new abilities or attributes and recapitulate early stages of embryogenesis. Our findings document how malignant tissues reactivated ancestral storage memory and elaborate inside tumor glands spiral- pyramidal-fractal chiral crystals (Tc) as geometric attractors proteins and biomimicry the primitive cellular blastocyst embryoblast fluid-filled cavity. The resultant evolutionary embryoblast-like entity has higher survivability and spatial cephalic-caudal growth organization with pluripotentiality that carry the correct DNA instructions to repair, and regenerate. The isolation and manipulation of these order structures can guide and control the regenerative pathway mechanism in human tumors as follows: modify and reprogram the phenotype of the tumor where these entities are generated, establish a reverse primordial microscopic mold to use the swirlonic collective behavior of cellular building blocks to regenerate injured tissues, convert cancer cells to a normal phenotype through regeneration using the organizational level and scale properties of reverse genetic guidance, global control of mitotic activity and morphogenetic movements avoiding their spread and metastasis, determining a better life prognosis for patients who incubate these entities in their tumors compared to those who do not express them. An emergent self-repair order structure, biological template to develop targeted therapeutic alternatives not only in cancer but also in treatment of autoimmune, viral diseases, and in regenerative medicine and rejuvenation.

Since the end of 2020, the mass vaccination has been actively promoted and seemed to be effective to bring the COVID-19 pandemic under control. However, the fact of immunity waning and the possible existence of antibody-dependent enhancement (ADE) make the situation uncertain. We developed a dynamic model of COVID-19 incorporating vaccination and immunity waning, which was calibrated by using the data of accumulative vaccine doses administered and the COVID-19 epidemic in 2020 in mainland China. We explored how long the current vaccination program can prevent China in a low risk of resurgence, and how ADE affects the long-term trajectory of COVID-19 epidemics. The prediction suggests that the vaccination coverage with at least one dose reach 95.87%, and with two-doses reach 77.92% on August 31, 2021. However, even with the mass vaccination, randomly introducing infected cases in the post-vaccination period can result in large outbreaks quickly in the presence of immunity waning, particularly for SARS-CoV-2 variants with higher transmission ability. The results showed that with the current vaccination program and a proportion of 50% population wearing masks, mainland China can be protected in a low risk of resurgence till 2023/01/18. However, ADE effect and higher transmission ability for variants would significantly shorten the protective period for more than 1 year. Furthermore, intermittent outbreaks can occur while the peak values of the subsequential outbreaks are decreasing, meaning that subsequential outbreaks boosted the immunity in the population level, which further indicating that catching-up vaccination program can help to mitigate the possible outbreaks, even avoid the outbreaks. The findings reveal that integrated effects of multiple factors, including immunity waning, ADE, relaxed interventions, and higher transmission ability of variants, make the control of COVID-19 much more difficult. We should get ready for a long struggle with COVID-19, and should not totally rely on COVID-19 vaccine.

Dopamine (DA) signals play critical roles in reward-related behavior, decision making, and learning. Yet the mainstream notion that DA signals are encoded by the temporal dynamics of individual DA cell activity is increasingly contested with data supporting that DA signals prefer to be encoded by the spatial organization of DA neuron populations. However, how distributed and parallel excitatory afferent inputs simultaneously induce burst synchronization (BS) is unclear. Our previous work implies that the burst could presumably transition from an integrator to a resonator if the excitatory inputs increase further. Here the responses of networked DA neurons to different intensity of excitatory inputs are investigated. It is found that as NMDA conductance increases, the network will transition from resting state to burst asynchronization (BA) state and then to BS state, showing a bounded BA and BS region in the NMDA conductance space. Furthermore, it is found that as muscarinic receptors modulated Ca2+ dependent cationic (CAN) conductance increases, both boundaries between resting and BA, and between BA and BS gradually decrease. Phase plane analysis on DA reduced model unveils that the burst transition to a resonator underpins the changes in the network dynamics. Slow-fast dissection analysis on DA full model uncovers that the underlying mechanism of the roles and synergy of NMDA and muscarinic receptors in inducing the burst transition emerge from the enlargement of nonlinear positive feedback relationship between more Ca2+ influx provided by additional NMDA current and more ICAN modulated by added muscarinic receptors. Moreover, the lag in DA volume transmission has no effect on excitatory inputs-elicited resonator BS except for requiring more excitatory inputs. These findings shed new lights on understanding the collective behavior of DA cells population regulated by the distributed excitatory inputs, and might provide a new perspective for understanding the abnormal DA release in pathological states. Author summaryThe importance of DA signals is beyond doubt, so their encoding mechanism has very important biological significance and draws widespread attention. Yet the mainstream notion that DA cells individual provide a uniform, broadly distributed signal is increasingly contested with data supporting both homogeneity across dopamine cell activity and diversity in DA signals in target regions. Our article proposes that diverse distributed and parallel excitatory inputs can not only regulate the temporal dynamics of individual DA cell activity, but also simultaneously and synergistically regulate the network dynamics of DA cell populations by changing the local dynamics of DA cells, namely the burst transition from integrators to resonators. According to our perspective, many data that are difficult to interpret by the notion of the DA neuron individual coding can be well explained, such as burst asynchronization coding DA ramping signals, the scale of burst synchronization coding the amplitude of phase DA release, inhibitory DA autoreceptors facilitating resonator burst synchronization by postinhibitory rebound, etc. This study aims to elucidate the working mechanism of the DA system in physiological states such as positive reinforcement, and then to provide a new research perspective and foundation for understanding the abnormal DA release in pathological states.

Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a robust irregular macroscopic dynamics. The resulting, strongly synchronized, regime is sustained by a homeostatic mechanism induced by the shape of the phase-response curve combined with adaptive coupling strength, included to account for energy dissipated by the pulse emission. The proposed setup mimicks a neural network composed of excitatory and inhibitory neurons.

Brain circuits display modular architecture at different scales of organization. Such neural assemblies are typically associated to functional specialization but the mechanisms leading to their emergence and consolidation still remain elusive. In this paper we investigate the role of inhibition in structuring new neural assemblies driven by the entrainment to various inputs. In particular, we focus on the role of partially synchronized dynamics for the creation and maintenance of structural modules in neural circuits by considering a network of excitatory and inhibitory{theta} -neurons with plastic Hebbian synapses. The learning process consists of an entrainment to temporally alternating stimuli that are applied to separate regions of the network. This entrainment leads to the emergence of modular structures. Contrary to common practice in artificial neural networks - where the acquired weights are typically frozen after the learning session - we allow for synaptic adaptation even after the learning phase. We find that the presence of inhibitory neurons in the network is crucial for the emergence and the post-learning consolidation of the modular structures. Indeed networks made of purely excitatory neurons or of neurons not respecting Dales principle are unable to form or maintain the modular architecture induced by the entrained stimuli. We also demonstrate that the number of inhibitory neurons in the network is directly related to the maximal number of neural assemblies that can be consolidated, supporting the idea that inhibition has a direct impact on the memory capacity of the neural network.

The widely-accepted hallmark pathology of Parkinsons disease (PD) is the presence of Lewy bodies (LB) with characteristic abnormal aggregated -synuclein (Syn). Growing physiological evidences suggest that there is a pivotal role for the autophagy-lysosome pathway in the clearance of misfolded Syn (Syn*) for maintaining homeostasis and neural cell function. In this work, we establish a new mathematical model for Syn* degradation through the autophagy pathway. The qualitative simulations discover the tri-stability phenomena and dynamical behaviors of Syn*, i.e., the coexistence of three stable steady states, in which the lower, medium and upper steady states correspond to the healthy, critical and diseased stages of pathological mechanism of PD, respectively. Diverse analyses on codimension-1 and -2 bifurcations suggest that autophagy can control the switches among the stable steady states for the aggregation of Syn*. It is also found that the double negative crosstalk feedback between autophagy and apoptosis is important to the robustness of tri-stability of Syn* for this biodynamic system. Our novel results may be valuable for making further therapeutic strategies in prevention and treatment for PD. Author summarySyn* is one of the most and primary remarkable targets for the universal neurodegenerative disease of PD. Efficient clearance mechanism of autophagy, contains a lot of molecular components to maintain the cellular homeostasis and cell renewal, could be the possible therapy for PD. Understand the complexity of autophagy in degrading Syn* requires the integration of both theoretical and experimental points of view. Here, we have proposed a novel mathematical model that analyses the temporal and dynamic behaviors of the biosystem for autophagy degrades Syn* to access PD states. The model explains that the tri-stability is of particularly relevance to this biosystem that switch among the healthy, critical and disease states, and captures that the critical intermedium state exits for preventing the system transform healthy to disease state directly, and further illustrates that the molecular signaling feedback loops of autophagy may be important for the robustness of tri-stability. Our work deepens the researches of PD by uncovering the important buffering medium state and providing promising potential therapeutic insights.

Information experiences complex transformation processes in the brain, involving various errors. A daunting and critical challenge in neuroscience is to understand the origin of these errors and their effects on neural information processing. While previous efforts have made substantial progresses in studying the information errors in bounded, unreliable and noisy transformation cases, it still remains elusive whether the neural system is inherently error-free under an ideal and noise-free condition. This work brings the controversy to an end with a negative answer. We propose a novel neural information confusion theory, indicating the widespread presence of information confusion phenomenon after the end of transmission process, which originates from innate neuron characteristics rather than external noises. Then, we reformulate the definition of zero-error capacity under the context of neuroscience, presenting an optimal upper bound of the zero-error transformation rates determined by the tuning properties of neurons. By applying this theory to neural coding analysis, we unveil the multi-dimensional impacts of information confusion on neural coding. Although it reduces the variability of neural responses and limits mutual information, it controls the stimulus-irrelevant neural activities and improves the interpretability of neural responses based on stimuli. Together, the present study discovers an inherent and ubiquitous precision limitation of neural information transformation, which shapes the coding process by neural ensembles. These discoveries reveal that the neural system is intrinsically error-prone in information processing even in the most ideal cases. Author summaryOne of the most central challenges in neuroscience is to understand the information processing capacity of the neural system. Decades of efforts have identified various errors in nonideal neural information processing cases, indicating that the neural system is not optimal in information processing because of the widespread presences of external noises and limitations. These incredible progresses, however, can not address the problem about whether the neural system is essentially error-free and optimal under ideal information processing conditions, leading to extensive controversies in neuroscience. Our work brings this well-known controversy to an end with a negative answer. We demonstrate that the neural system is intrinsically error-prone in information processing even in the most ideal cases, challenging the conventional ideas about the superior neural information processing capacity. We further indicate that the neural coding process is shaped by this innate limit, revealing how the characteristics of neural information functions and further cognitive functions are determined by the inherent limitation of the neural system.

Grasping the fundamental dynamic property is a crucial approach for understanding living systems. Here we conduct a comprehensive study into the relationship between regulatory modes and dynamic features of gene networks. Our findings indicate that conditional constraints and competition, corresponding to canalizing and threshold regulating modes respectively, play pivotal roles in driving gene networks towards criticality. Particularly, they effectively rescue biosystems from disordered area as source of evolutionary driving force. By employing variant Kauffman models, order parameters, and stability analysis, we provide sufficient numerical evidence demonstrating the diverse and distinctive capabilities of regulatory modes in stabilizing systems. Our findings give the most systematic analysis to date on the dynamic atlas of regulatory modes, offering a framework-independent proof of genetic networks operating at the edge of chaos with evolutionary implications. Furthermore, we discus the bridge between criticality and canalizing/threshold regulating modes and propose a reasonable scheme for generating model.

We are concerned about the main encoding granule cells (GCs) in the hippocampal dentate gyrus (DG). Young immature GCs (imGCs) appear through adult neurogenesis. In comparison to the mature GCs (mGCs) (born during development), the imGCs show high activation due to lower firing threshold. On the other hand, they receive low excitatory drive from the entorhinal cortex via perforant paths and from the hilar mossy cells with lower connection probability pc (= 20 x %) (x : synaptic connectivity fraction; 0 [≤] x [≤] 1) than the mGCs with the connection probability pc (= 20 %). Thus, the effect of low excitatory innervation (reducing activation degree) for the imGCs counteracts the effect of their high excitability. We consider a spiking neural network for the DG, incorporating both the mGCs and the imGCs. With decreasing x from 1 to 0, we investigate the effect of young adult-born imGCs on the sparsely synchronized rhythms (SSRs) of the GCs (mGCs, imGC, and whole GCs). For each x, population and individual firing behaviors in the SSRs are characterized in terms of the amplitude measure [Formula] (X = m, im, w for the mGCs, the imGCs, and the whole GCs, respectively) (representing the population synchronization degree) and the random phase-locking degree [Formula] (characterizing the regularity of individual single-cell discharges), respectively. We also note that, for 0 [≤] x [≤] 1, the mGCs and the imGCs exhibit pattern separation (i.e., a process of transforming similar input patterns into less similar output patterns) and pattern integration (making association between patterns), respectively. Quantitative relationship between SSRs and pattern separation and integration is also discussed. PACS numbers87.19.lj, 87.19.lm, 87.19.lv