The Parameters Estimation to Realize Desired Periodic Synchronization in Coupled Nonlinear Oscillators

Abstract

It is known that the synchronization phenomenon emerges from the coupling system of some nonlinear oscillations, and that behavior of synchronization depends on coupling parameters. At first, we propose the method to estimate coupling parameters which realize synchronization starting at the desired time by solving the parameter optimization problem. On the other hand, the periodic cycle of nonlinear oscillation depends on its parameters (bifurcation parameters). The relation between a periodic cycle and bifurcation parameters can be known by describing the bifurcation diagram. Secondly, we formulate the parameter optimization problem to estimate the bifurcation parameters which realize the desired periodic cycle without a bifurcation diagram. Finally, we formulate the integrated type of parametr optimization problem to find the bifurcation parameters of nonlinear oscillations with the desired periodic cycle, as well as the coupling parameters to realize the desired synchronization simultaneously. In order to solve this problem, we use the gradient method based on variational method. As a result of this method, we can realize the synchronization with desired periodic cycle starting at the desired time.