Wave processes in a ring of memristively coupled self-excited oscillators

Abstract

The purpose of this work is to reveal intrinsic peculiarities of the dynamics and spatial structure formation in an ensemble of the coupled van der Pol self-oscillators in a case of memristive coupling. Two models of memristive coupling are considered: an idealised memristive model and a real one exhibiting the effect of «forgetting» of an initial state after a long time. Methods. Numerical simulation of the equations describing the system under study by means of the fourthorder Runge–Kutta method is carried out. Further exploration consists in plotting and analysis of space-time diagrams and instantaneous spatial profiles of dynamical regimes obtained by means of varying the initial conditions and parameter values. Results. It is shown that the shape of an instantaneous spatial profile fully depends on initial conditions in a case of ideal memristive coupling. Choosing the initial conditions, one can realize coexistence of different clusters with qualitatively different kinds of the dynamics (for instance, coexisting travelling waves and regimes of full synchronization). Such a phenomenon disappears in a system with the «forgetting» effect. Conclusion. The properties of memristive coupling strongly impact the behaviour of interacting self-oscillators. The system with ideal memristive coupling is very sensitive to initial conditions. It allows to control the dynamics in a broad range and to change the spatial profile form varying the initial conditions.

Keywords

• ensemble
• van der pol oscillator
• memristor
• memristive coupling
• spatial structures