A sufficient synchronization condition for oscillators coupled diffusively by nonlinear passive systems - Robin Lautenbacher; Jonas Röhrig; Karlheinz Ochs; Ralf Köhl (Discover Applied Sciences)
Abstract We study identical semi-passive systems coupled pairwise by heterogeneous, linear or nonlinear passive systems, including systems with memory such as memristive systems. The semi-passive systems are assumed to satisfy a certain input–output symmetry and can for instance be oscillators with an asymptotically stable limit cycle or systems with asymptotically stable equilibrium, but also chaotic systems or neuronal oscillators. We represent the system of coupled semi-passive systems by a graph. The semi-passive systems are associated with the nodes of that graph and the nonlinear passive systems are associated with the graphs edges. To each such system we associate a weight defined as the largest value w.r.t. which the system is input- or output-passive. We derive a sufficient condition for synchronization that is phrased in terms of the algebraic connectivity of the weighted coupling graph, a generalized one-sided Lipschitz-condition associated to the semi-passive system and a constant related to its linear input–output-behavior. We also derive a sufficient condition for output synchronization in a border-line case where our main condition is not applicable.