Dynamical manifold dimensionality as characterization measure of chimera states in bursting neuronal networks

IF 3.4 2区 数学 Q1 MATHEMATICS, APPLIED
Olesia Dogonasheva , Daniil Radushev , Boris Gutkin , Denis Zakharov
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Abstract

Methods that distinguish dynamical regimes in networks of active elements make it possible to design the dynamics of models of realistic networks. A particularly salient example of such dynamics is partial synchronization, which may play a pivotal role in emergent behaviors of biological neural networks. Such emergent partial synchronization in structurally homogeneous networks is commonly denoted as chimera states. While several methods for detecting chimeras in networks of spiking neurons have been proposed, these are less effective when applied to networks of bursting neurons. In this study, we propose the correlation dimension as a novel approach that can be employed to identify dynamic network states. To assess the viability of this new method, we study networks of intrinsically bursting Hindmarsh–Rose neurons with non-local connections. In comparison to other measures of chimera states, the correlation dimension effectively characterizes chimeras in burst neurons, whether the incoherence arises in spikes or bursts. The generality of dimensionality measures inherent in the correlation dimension renders this approach applicable to a wide range of dynamic systems, thereby facilitating the comparison of simulated and experimental data. This methodology enhances our ability to tune and simulate intricate network processes, ultimately contributing to a deeper understanding of neural dynamics.

将动态流形维度作为突发性神经元网络中嵌合体状态的表征量度
区分活跃元素网络动态机制的方法使得设计现实网络模型的动态机制成为可能。这种动力学的一个特别突出的例子是部分同步,它可能在生物神经网络的突发行为中发挥关键作用。在结构均匀的网络中出现的这种部分同步通常被称为嵌合态。虽然已经提出了几种在尖峰神经元网络中检测嵌合体的方法,但这些方法应用于猝发神经元网络时效果不佳。在本研究中,我们提出了相关维度作为一种可用于识别动态网络状态的新方法。为了评估这种新方法的可行性,我们研究了具有非局部连接的内在猝发 Hindmarsh-Rose 神经元网络。与其他测量嵌合体状态的方法相比,相关维度能有效描述猝发神经元中嵌合体的特征,无论不一致性产生于尖峰还是猝发。相关维度所固有的维度测量的通用性使这种方法适用于各种动态系统,从而促进了模拟数据和实验数据的比较。这种方法提高了我们调整和模拟复杂网络过程的能力,最终有助于加深对神经动力学的理解。
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来源期刊
Communications in Nonlinear Science and Numerical Simulation
Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
6.80
自引率
7.70%
发文量
378
审稿时长
78 days
期刊介绍: The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.
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