Complexity in time-delay networks of multiple interacting neural groups

Xiaochen Mao; Weijie Ding; Xiangyu Zhou; Song Wang; Xingyong Li; Xiaochen Mao; Weijie Ding; Xiangyu Zhou; Song Wang; Xingyong Li

doi:10.3934/era.2021022

Electronic Research Archive

2021, Volume 29, Issue 5: 2973-2985. doi: 10.3934/era.2021022

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Complexity in time-delay networks of multiple interacting neural groups

Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, China

Received: 01 December 2020 Revised: 01 January 2021 Published: 15 March 2021
70K50, 92B20, 34Kxx

Coupled networks are common in diverse real-world systems and the dynamical properties are crucial for their function and application. This paper focuses on the behaviors of a network consisting of mutually coupled neural groups and time-delayed interactions. These interacting groups can include different sets of nodes and topological architecture, respectively. The local and global stability of the system are analyzed and the stable regions and bifurcation curves in parameter planes are obtained. Different patterns of bifurcated solutions arising from trivial and non-trivial equilibrium points are given, such as the coexistence of non-trivial equilibrium points and periodic responses and multiple coexisting periodic orbits. The bifurcation diagrams are shown and plenty of complex dynamic phenomena are observed, such as multi-period oscillations and multiple coexisting attractors.
- Multiplex networks,
- time delays,
- bifurcations,
- complicated oscillations
Citation: Xiaochen Mao, Weijie Ding, Xiangyu Zhou, Song Wang, Xingyong Li. Complexity in time-delay networks of multiple interacting neural groups[J]. Electronic Research Archive, 2021, 29(5): 2973-2985. doi: 10.3934/era.2021022

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Abstract

Coupled networks are common in diverse real-world systems and the dynamical properties are crucial for their function and application. This paper focuses on the behaviors of a network consisting of mutually coupled neural groups and time-delayed interactions. These interacting groups can include different sets of nodes and topological architecture, respectively. The local and global stability of the system are analyzed and the stable regions and bifurcation curves in parameter planes are obtained. Different patterns of bifurcated solutions arising from trivial and non-trivial equilibrium points are given, such as the coexistence of non-trivial equilibrium points and periodic responses and multiple coexisting periodic orbits. The bifurcation diagrams are shown and plenty of complex dynamic phenomena are observed, such as multi-period oscillations and multiple coexisting attractors.

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