Nonlinear dynamics equations and chaos

Abstract

Nonlinear dynamics and chaotic systems have been of great interest to many scientists and engineers over the past two decades. Many nonlinear systems are a result of mathematical models of physical and biological systems that possess inherent nonlinear properties. In this paper, we focus our attention on a second-degree nonlinear differential equation with a sinusoidal forcing function and constant coefficients; such equations, which are commonly employed for mathematical modeling of biological systems usually possess inherent nonlinear properties. We show that the second-degree nonlinear differential equation system could be aperiodic and therefore the long-term behavior is not predictable. However, in the case of the increased frequency of the sinusoidal input, the system shows somewhat periodic, convergent behavior. The simulations demonstrate how small, seemingly insignificant changes to the parameters (e.g., initial conditions) can dramatically alter the system response.