GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF A SECOND-ORDER DUFFING EQUATION WITH POISON STABLE COEFFICIENT
Abstract
This paper presents a comprehensive analysis of the global asymptotic stability of solutions to a second-order Duffing-type differential equation with a Poisson-stable coefficient. The Duffing equation, widely recognized as a fundamental nonlinear oscillator model, exhibits increased dynamical complexity when subjected to non-autonomous and time-varying perturbations such as Poisson stability. In this work, we extended existing stability results by constructing an appropriate Lyapunov function and employing comparison principles to derive sufficient conditions that guarantee the asymptotic convergence of all solutions to the trivial equilibrium. The approach not only addresses the inherent challenges posed by the recurrent and non-periodic nature of Poisson-stable functions but also provides a rigorous framework for analyzing stability in broader classes of nonlinear, non-autonomous systems. The theoretical findings presented here contribute to the understanding of oscillatory behavior in complex dynamical models and have potential implications for engineering and applied sciences where stability under recurrent external influences is critical.
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