Investigating the effect of changes in neuronal connectivity on the brain's behavior is of interest in neuroscience studies. Complex network theory is one of the most capable tools to study the effects of these changes on collective brain behavior. By using complex networks, the neural structure, function, and dynamics can be analyzed. In this context, various frameworks can be used to mimic neural networks, among which multi-layer networks are a proper one. Compared to single-layer models, multi-layer networks can provide a more realistic model of the brain due to their high complexity and dimensionality. This paper examines the effect of changes in asymmetry coupling on the behaviors of a multi-layer neuronal network. To this aim, a two-layer network is considered as a minimum model of left and right cerebral hemispheres communicated with the corpus callosum. The chaotic model of Hindmarsh-Rose is taken as the dynamics of the nodes. Only two neurons of each layer connect two layers of the network. In this model, it is assumed that the layers have different coupling strengths, so the effect of each coupling change on network behavior can be analyzed. As a result, the projection of the nodes is plotted for several coupling strengths to investigate how the asymmetry coupling influences the network behaviors. It is observed that although no coexisting attractor is present in the Hindmarsh-Rose model, an asymmetry in couplings causes the emergence of different attractors. The bifurcation diagrams of one node of each layer are presented to show the variation of the dynamics due to coupling changes. For further analysis, the network synchronization is investigated by computing intra-layer and inter-layer errors. Calculating these errors shows that the network can be synchronized only for large enough symmetric coupling.

Center for Basic and Applied Research Faculty of Informatics and Management University of Hradec Kralove Hradec Kralove Czechia

Centre for Computational Biology Chennai Institute of Technology Chennai 600069 India

Centre for Nonlinear Systems Chennai Institute of Technology Chennai 600069 India

College of Engineering and Science Victoria University Melbourne Australia

Department of Biomedical Engineering and Measurement Faculty of Mechanical Engineering Technical University of Kosice Slovakia

Department of Computer Technology Engineering College of Information Technology Imam Ja'afar Al Sadiq University Baghdad 10001 Iraq

Institute of Technology and Business in Ceske Budejovice Ceske Budejovice Czechia

School of Engineering Monash University Selangor Malaysia

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