Non-linear dynamics equations and chaos

Nonlinear dynamics and chaotic systems are of great interest to many scientists and engineers in past two decades. Many non-linear 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 non-linear differential equation with asinusoidal 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 non-linear 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.