Chaos最新文献

{"title":"Nonlinear mechanisms for enhanced and synchronized post-inhibitory rebound spiking associated with seizures in an inhibitory-excitatory neuronal network.","authors":"Yanbing Jia, Huaguang Gu, Xianjun Wang","doi":"10.1063/5.0232718","DOIUrl":"https://doi.org/10.1063/5.0232718","url":null,"abstract":"<p><p>Recent experimental observations on seizures showed that the optogenetic activation of inhibitory interneurons cannot suppress but enhance the frequency and synchronization of spiking of excitatory pyramidal neurons, i.e., synchronized post-inhibitory rebound (PIR) spiking. This complex phenomenon presents paradoxical functions of interneurons and novel etiologies of seizures. In the present study, nonlinear mechanisms and conditions of the synchronized PIR spiking are obtained in a network model of inhibitory interneurons and excitatory pyramidal neurons. Pyramidal neurons with low spiking frequency near the bifurcation, characterized by small conductances (gh) of the hyperpolarization-activated cation (Ih) current and small applied current, are easy to generate PIR spiking. Strong optogenetic stimulation activating interneurons with high spiking frequency and inhibitory synapses with large conductances contribute to the PIR spiking. Moreover, after the optogenetic stimulation, the excitatory synaptic current from pyramidal neurons to interneurons can induce spiking of interneurons to reduce the PIR spiking. Reducing the membrane potential of interneurons can enhance the range of excitatory synaptic conductances for PIR spiking. The PIR spiking can be interpreted by complex nonlinear interactions between the hyperpolarization activation of the Ih current and membrane potential modulated by gh and inhibitory stimulation. Furthermore, higher synchronization degrees of the PIR spiking appear for the spiking with lower frequency. During the inhibitory stimulation, pyramidal neurons become silence with a small difference in membrane potential, which remains within long intervals between spikes and results in strong synchronization after stimulation. The nonlinear mechanisms and conditions of the synchronized PIR spiking are helpful for recognizing and modulating seizures.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143604003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantifying wave propagation in a chain of FitzHugh-Nagumo neurons.","authors":"L Messee Goulefack, C Masoller, R Yamapi, C Anteneodo","doi":"10.1063/5.0239976","DOIUrl":"10.1063/5.0239976","url":null,"abstract":"<p><p>Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this work, we examine a simple \"toy model\" of an excitable medium, a linear chain of diffusely coupled FitzHugh-Nagumo neurons, and analyze the transmission of a sinusoidal signal injected into one of the neurons at the ends of the chain. We measure to what extent the propagation of the wave reaching the opposite end is affected by the frequency and amplitude of the signal, the number of neurons in the chain, and the strength of their mutual diffusive coupling. To quantify these effects, we measure the cross correlation between the time series of the membrane potentials of the end neurons. This measure allows us to detect the values of the parameters that delimit different propagation regimes.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143604044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heterogeneous K-core percolation on hypergraphs.","authors":"Dandan Zhao, Wenjia Xi, Bo Zhang, Cheng Qian, Yifan Zhao, Shenhong Li, Hao Peng, Wei Wang","doi":"10.1063/5.0245871","DOIUrl":"10.1063/5.0245871","url":null,"abstract":"<p><p>In complex systems, there are pairwise and multiple interactions among elements, which can be described as hypergraphs. K-core percolation is widely utilized in the investigation of the robustness of systems subject to random or targeted attacks. However, the robustness of nodes usually correlates with their characteristics, such as degree, and exhibits heterogeneity while lacking a theoretical study on the K-core percolation on a hypergraph. To this end, we constructed a hyperedge K-core percolation model that introduces heterogeneity parameters to divide the active hyperedges into two parts, where hyperedges are inactive unless they have a certain number of active nodes. In the stage of pruning process, when the number of active nodes contained in a hyperedge is less than its set value, it will be pruned, which will result in the deletion of other hyperedges and ultimately trigger cascading failures. We studied the magnitude of the giant connected component and the percolation threshold of the model by mapping a random hypergraph to a factor graph. Subsequently, we conducted a large number of simulation experiments, and the theoretical values matched well with the simulated values. The heterogeneity parameters of the proposed model have a significant impact on the magnitude of the giant connected component and the type of phase transition in the network. We found that decreasing the value of heterogeneity parameters renders the network more fragile, while increasing the value of heterogeneity parameters makes it more resilient under random attacks. Meanwhile, as the heterogeneity parameter decreases to 0, it may cause a change in the nature of network phase transition, and the network shows a hybrid transition.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143717801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diffusing diffusivity model of a polymer moving on a spherical surface.","authors":"Xinyi Wu, Daxin Nie, Weihua Deng","doi":"10.1063/5.0251095","DOIUrl":"https://doi.org/10.1063/5.0251095","url":null,"abstract":"<p><p>The movement of a polymer is modeled by Brownian motion accompanied with a fluctuating diffusion coefficient when the polymer is in contact with a chemostatted monomer bath triggering the chain polymerization, which is called a diffusing diffusivity (DD) model. In this paper, we extend the DD model from three dimensional Euclidean space to a two dimensional spherical surface. The DD model on the spherical surface is described by a coupling Langevin system in the directions of longitude and latitude, while the diffusion coefficient is characterized by the birth and death chain. Then, the Fokker-Planck and Feynman-Kac equations for the DD model on the spherical surface, respectively, governing the probability density functions (PDFs) of the two statistical observables, position and functional, are derived. Finally, we use two ways to calculate the PDFs of some statistical observables, i.e., applying a Monte Carlo method to simulate the DD model and a spectral method to solve the Fokker-Planck and Feynman-Kac equations. In fact, the unification of the numerical results of the two ways also confirms the correctness of the built equations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143572021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interactions of fractional solitons with local defects: Stabilization and scattering.","authors":"Thawatchai Mayteevarunyoo, Boris A Malomed","doi":"10.1063/5.0259305","DOIUrl":"https://doi.org/10.1063/5.0259305","url":null,"abstract":"<p><p>Stability is an essential problem in theoretical and experimental studies of solitons in nonlinear media with fractional diffraction, which is represented by the Riesz derivative with Lévy index (LI) α, taking values α<2. Fractional solitons are unstable at α≤1 or α≤2 in uniform one-dimensional media with the cubic or quintic self-focusing, respectively. We demonstrate that, in these cases, the solitons may be effectively stabilized by pinning to a delta-functional trapping potential (attractive defect), which is a relevant setting in optical waveguides with the effective fractional diffraction. Using the respective fractional nonlinear Schrödinger equation with the delta-functional potential term, we find that, in the case of the cubic self-focusing, the fractional solitons are fully stabilized by the pinning to the defect for α=1 and partly stabilized for α<1. In the case of the quintic self-focusing, the full and partial stabilization are found for α=2 and α<2, respectively. In both cases, the instability boundary is exactly predicted by the Vakhitov-Kolokolov criterion. Unstable solitons spontaneously transform into oscillating breathers. A variational approximation (VA) is elaborated parallel to the numerical analysis, with a conclusion that the VA produces accurate results for lower LI values, i.e., stronger fractionality. In the cubic medium, collisions of traveling stable solitons with repulsive and attractive defects are addressed too, demonstrating outcomes in the form of rebound, splitting, and passage.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143662974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A minimal model for multigroup adaptive SIS epidemics.","authors":"Massimo A Achterberg, Mattia Sensi, Sara Sottile","doi":"10.1063/5.0246228","DOIUrl":"https://doi.org/10.1063/5.0246228","url":null,"abstract":"<p><p>We propose a generalization of the adaptive N-Intertwined Mean-Field Approximation (aNIMFA) model studied in Achterberg and Sensi [Nonlinear Dyn. 111, 12657-12670 (2023)] to a heterogeneous network of communities. In particular, the multigroup aNIMFA model describes the impact of both local and global disease awareness on the spread of a disease in a network. We obtain results on the existence and stability of the equilibria of the system, in terms of the basic reproduction number R0. Assuming individuals have no reason to decrease their contacts in the absence of disease, we show that the basic reproduction number R0 is equivalent to the basic reproduction number of the NIMFA model on static networks. Based on numerical simulations, we demonstrate that with just two communities periodic behavior can occur, which contrasts the case with only a single community, in which periodicity was ruled out analytically. We also find that breaking connections between communities is more fruitful compared to breaking connections within communities to reduce the disease outbreak on dense networks, but both strategies are viable in networks with fewer links. Finally, we emphasize that our method of modeling adaptivity is not limited to Susceptible-Infected-Susceptible models, but has huge potential to be applied in other compartmental models in epidemiology.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Devil's staircase inside shrimp-shaped regions reveals periodicity of plateau spikes and bursts.","authors":"Luiz F B Caixeta, Matheus H P Gonçalves, M H R Tragtenberg, Mauricio Girardi-Schappo","doi":"10.1063/5.0250342","DOIUrl":"https://doi.org/10.1063/5.0250342","url":null,"abstract":"<p><p>Slow-fast dynamics are intrinsically related to complex phenomena and are responsible for many of the homeostatic dynamics that keep biological systems healthy functioning. We study a discrete-time membrane potential model that can generate a diverse set of spiking behavior depending on the choice of slow-fast time scales, from fast spiking to bursting, or plateau action potentials-also known as cardiac spikes since they are characteristic in heart myocytes. The plateau of cardiac spikes can lose stability, generating early or delayed afterdepolarizations (EADs and DADs, respectively), both of which are related to cardiac arrhythmia. We show the periodicity changes along the transition from the healthy action potentials to these impaired oscillations. We show that while EADs are mainly periodic attractors, DADs usually come with chaos. EADs are found inside shrimp-shaped regions of the parameter space. However, in our system, multiple periodic attractors live within a shrimp-shaped region, giving it an internal structure made of infinite transitions between periodicities forming a complete devil's staircase. Understanding the periodicity of plateau attractors in slow-fast systems could be useful in unveiling the characteristics of heart myocyte behaviors that are linked to cardiac arrhythmias.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-trivial generation and transmission of information in electronically designed logistic-map networks.","authors":"Caracé Gutiérrez, Cecilia Cabeza, Nicolás Rubido","doi":"10.1063/5.0238711","DOIUrl":"https://doi.org/10.1063/5.0238711","url":null,"abstract":"<p><p>In this work, we carry out a critical analysis of the information generated and transmitted in an electronic implementation of diffusively coupled logistic maps. Our implementation allows one to change the coupling configuration (i.e., the network) and fine-tune the coupling strength and map parameters, but has minimal electronic noise and parameter heterogeneity, which generates collective behaviors that differ from numerical simulations. In particular, we focus on analyzing two dynamical regimes and their dependence on the coupling configuration: one where there is a maximum of information generated and transmitted-corresponding to synchronization of chaotic orbits-and another where information is generated but (practically) not transmitted-corresponding to spatiotemporal chaos. We use Shannon entropy to quantify information generation and mutual information to quantify information transmission. To characterize the two dynamical regimes, we introduce a conditional joint entropy that uses both quantities (entropy and mutual information) and analyze its values for 60 different coupling configurations involving 6 and 12 coupled maps. We find that 90% of the configurations exhibit chaotic synchronization and 92% spatiotemporal chaos, which emerges preceding the chaotic synchronous regime that requires strong coupling strengths. Our results also highlight the coupling configurations that maximize the conditional joint entropy in these regimes without requiring a densely coupled system, which has practical implications (since introducing couplings between units can be costly). Overall, our work contributes to understand the relevance that the network structure has on the generation and transmission of information in complex systems.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143699851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Introduction to Focus Issue: Data-driven models and analysis of complex systems.","authors":"Johann H Martínez, Klaus Lehnertz, Nicolás Rubido","doi":"10.1063/5.0263794","DOIUrl":"https://doi.org/10.1063/5.0263794","url":null,"abstract":"<p><p>This Focus Issue highlights recent advances in the study of complex systems, with a particular emphasis on data-driven research. Our editorial explores a diverse array of topics, including financial markets, electricity pricing, power grids, lasers, the Earth's climate, hydrology, neuronal assemblies and the brain, biomedicine, complex networks, real-world hypergraphs, animal behavior, and social media. This diversity underscores the broad applicability of complex systems research. Here, we summarize the 47 published works under this Focus Issue, which employ state-of-the-art or novel methodologies in machine learning, higher-order correlations, control theory, embeddings, information theory, symmetry analysis, extreme event modeling, time series analysis, fractal techniques, Markov chains, and persistent homology, to name a few. These methods have substantially enhanced our understanding of the intricate dynamics of complex systems. Furthermore, the published works demonstrate the potential of data-driven approaches to revolutionize the study of complex systems, paving the way for future research directions and breakthroughs at the intersection of complexity science and the digital era of data.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143630222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcation and chaotic dynamics in a spatiotemporal epidemic model with delayed optimal control, stochastic process, and sensitivity analysis.","authors":"Arjun Kumar, Uma S Dubey, Balram Dubey","doi":"10.1063/5.0251992","DOIUrl":"10.1063/5.0251992","url":null,"abstract":"<p><p>This study introduces an epidemic model with a Beddington-DeAngelis-type incidence rate and Holling type II treatment rate. The Beddington-DeAngelis incidence rate is used to evaluate the effectiveness of inhibitory measures implemented by susceptible and infected individuals. Moreover, the choice of Holling type II treatment rate in our model aims to assess the impact of limited treatment facilities in the context of disease outbreaks. First, the well-posed nature of the model is analyzed, and then, we further investigated the local and global stability analysis along with bifurcation of co-dimensions 1 (transcritical, Hopf, saddle-node) and 2 (Bogdanov-Takens, generalized Hopf) for the system. Moreover, we incorporate a time-delayed model to investigate the effect of incubation delay on disease transmission. We provide a rigorous demonstration of the existence of chaos and establish the conditions that lead to chaotic dynamics and chaos control. Additionally, sensitivity analysis is performed using partial rank correlation coefficient and extended Fourier amplitude sensitivity test methods. Furthermore, we delve into optimal control strategies using Pontryagin's maximum principle and assess the influence of delays in state and control parameters on model dynamics. Again, a stochastic epidemic model is formulated and analyzed using a continuous-time Markov chain model for infectious propagation. Analytical estimation of the likelihood of disease extinction and the occurrence of an epidemic is conducted using the branching process approximation. The spatial system presents a comprehensive stability analysis and yielding criteria for Turing instability. Moreover, we have generated the noise-induced pattern to assess the effect of white noise in the populations. Additionally, a case study has been conducted to estimate the model parameters, utilizing COVID-19 data from Poland and HIV/AIDS data from India. Finally, all theoretical results are validated through numerical simulations. This article extensively explores various modeling techniques, like deterministic, stochastic, statistical, pattern formation(noise-induced), model fitting, and other modeling perspectives, highlighting the significance of the inhibitory effects exerted by susceptible and infected populations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143718191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}