Spatiotemporal dynamics in a ring of N mutually coupled self-sustained systems.

In this paper, we consider the spatiotemporal dynamics in a ring of N mutually coupled self-sustained oscillators in the regular state. When there are no parameter mismatches, the good coupling parameters leading to full, partial, and no synchronization are derived using the properties of the variational equations of stability. The effects of the spatial dimension of the ring on the stability boundaries of the synchronized states are performed. Numerical simulations validate and complement the results of analytical investigations. The influences of coupling parameter mismatch on the forecasted stability boundaries are also highlighted.

Synchronization of two coupled self-excited systems with multi-limit cycles.

We analyze the stability and optimization of the synchronization process between two coupled self-excited systems modeled by the multi-limit cycles van der Pol oscillators through the case of an enzymatic substrate reaction with ferroelectric behavior in brain waves model. The one-way and two-way couplings synchronization are considered. The stability boundaries and expressions of the synchronization time are obtained using the properties of the Hill equation. Numerical simulations validate and complement the results of analytical investigations.

Synchronized states in a ring of mutually coupled self-sustained electrical oscillators.

We investigate in this paper different states of synchronization in a ring of mutually coupled self-sustained electrical oscillators. The good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability. A stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained. In both cases, the numerical simulation validates and complements the results of the analytical investigation.