In this paper, we explore numerically the impact of different types of inter-layer coupling on the dynamics of a two-layer multiplex network of coupled FitzHugh–Nagumo oscillators in the excitable regime. For this purpose, the cases of attractive, repulsive, and periodically modulated inter-layer coupling are considered. Coupled in the ring structure, the FitzHugh–Nagumo neurons demonstrate travelling wave regimes which are different for the attractive and repulsive intra-layer coupling. It is shown that the inter-layer coupling affects not only the frequency of oscillations of individual neurons but also the spatio-temporal structures in individual layers in different ways, depending on the sign of the inter-layer coupling. It is established that complete in-phase synchronization of travelling waves is well achieved in the presence of attractive inter-layer coupling, while the repulsive inter-layer coupling induces effective anti-phase synchronization of wave regimes. When the inter-layer coupling is periodically modulated, the wave structures in both layers are distorted, and clusters of coherent and incoherent dynamics can appear in the ring space. The paper was presented at PhysCon2024.

Andrei V. Bukh

Nataliya N. Nikishina

Eugene M. Elizarov

Galina I. Strelkova

Cybernetics and Physics

The scope of the journal includes:    -Nonlinear dynamics and control  -Complexity and self-organization  -Control of oscillations  -Control of chaos and bifurcations  -Control in thermodynamics  -Control of flows and turbulence  -Information Physics  -Cyber-physical systems  -Modeling and identification of physical systems  -Quantum information and control  -Analysis and control of complex networks  -Synchronization of systems and networks  -Control of mechanical and micromechanical systems  -Dynamics and control of plasma, beams, lasers, nanostructures  -Applications of cybernetic methods in chemistry, biology, other natural sciences    The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.

The journal "Cybernetics and Physics" covers a wide range of topics, including nonlinear dynamics and control, complexity and self-organization, control of oscillations, chaos and bifurcation control, thermodynamic control, control of flows and turbulence, information physics, cyber-physical systems, modeling and identification of physical systems, quantum information and control, analysis and control of complex networks, synchronization of systems and networks, control of mechanical and micromechanical systems, dynamics and control of plasma, beams, lasers, and nanostructures, as well as applications of cybernetic methods in chemistry, biology, and other natural sciences. We welcome papers that have a cybernetic flavor in physics and those that have a physical flavor in cybernetics. Cybernetics is understood to encompass not only control but also areas such as estimation, filtering, optimization, identification, information theory, pattern recognition, and other related fields.

《Cybernetics and Physics》期刊的范围包括：非线性动力学与控制、复杂性与自组织、振荡控制、混沌与分岔控制、热力学控制、流动与湍流控制、信息物理学、网络物理系统、物理系统的建模与识别、量子信息与控制、复杂网络的分析与控制、系统与网络的同步、机械与微机械系统的控制、等离子体、束流、激光、纳米结构的动力学与控制，以及在化学、生物学和其他自然科学中应用控制论方法。我们欢迎具有控制论特征的物理学论文以及具有物理学特征的控制论论文。控制论不仅包括控制，还涵盖估计、滤波、优化、识别、信息理论、模式识别及其他相关领域。

Interaction of travelling waves in multilayer networks

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