Delay-Independent Synchronization and Network Topology of Systems with Transmission Delay Couplings

Abstract

We investigate the relationship between graph topology and delay-independent synchronization occuring in networks of the identical nonlinear systems with transmission delays. In this paper, we show that if networks contain a cycle subgraph of an odd number of nodes, partial synchronization corresponding to the equitable graph partition with the fewest cells occurs for a sufficiently large coupling strength regardless of the length of time-delay. The validity of the obtained results are examined through numerical simulations of Hindmarsh-Rose neuron systems networks.

Keywords

• synchronization
• time-delay
• chaotic systems
• graph theory