Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems

摘要: This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the approach, differential equations of systems are discretized to obtain implicit maps, and mapping structure based on maps is employed flow. From structures, predicted analytically corresponding stability bifurcations determined through eigenvalue analysis. The by single-step discussed first, multistep also presented. Periodic time-delay maps. nodes discretization were treated both an interpolation direct integration. Based discrete with/without time-delay, Fourier series responses To demonstrate methodology, bifurcation tree period-1 motion chaos Duffing oscillator presented as sampled problem. this can be applied systems, which cannot solved directly analytical methods.