A design template for globally stable nonlinear oscillators with multiple dynamics

Abstract

In this study, a template is proposed for designing ordinary differential equation-based nonlinear oscillators. The template is a two-dimensional system with two control parameters and an energy function. By choosing the appropriate energy function, it is possible to obtain globally stable systems. These systems can be a gradient system, a Hamiltonian system, or a system with a stable limit cycle depending on the choice of control parameters. Hamiltonian and limit cycle cases can be used as a nonlinear oscillator for various applications. An example system is demonstrated by choosing a simple energy function and the obtained system is simulated to verify its dynamics. Hardware verification of the simulated system is performed with a field programmable gate array (FPGA) implementation.