Abstract
Nonlinear dynamics takes its origins from physics and applied mathematics [...]
Highlights
Mathematical modeling of physical systems, dedicated numerical methods, asymptotic methods in computations, interdisciplinary nonlinear nature of engineering problems, discontinuity driven nonlinear behavior, complex nonlinear dynamics, identification of nonlinear systems, optimization principles of nonlinear behavior, control schemes in nonlinear engineering systems, nonlinearity caused engineering problems, numerical methods in analysis of periodic and chaotic nonlinear systems
Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods
The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions
Summary
Numerical methods in analysis of periodic and chaotic nonlinear systems. These models are represented by both linear and nonlinear ordinary differential equations. “Exact” finite difference schemes, which are a special NSFD, are provided for the linear models while the NSFD rules are applied, based on Mickens’ idea of transferring nonlinear models into discrete schemes.
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