Open AccessComplexity in time-delay networks of multiple interacting neural groups
Author(s) -
Xiaochen Mao,
Wenchao Ding,
Xiangyu Zhou,
Song Wang,
Xingyong Li
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021022
Subject(s) - attractor , bifurcation , period (music) , stability (learning theory) , artificial neural network , topology (electrical circuits) , function (biology) , bifurcation diagram , mathematics , computer science , pure mathematics , statistical physics , physics , mathematical analysis , combinatorics , nonlinear system , artificial intelligence , evolutionary biology , acoustics , biology , quantum mechanics , machine learning
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.