Global bifurcation and chaos
WebUsing Crandall–Rabinowitz bifurcation theory, we investigate the steady-state bifurcation of the nonlinear system by choosing the prey-tactic sensitivity coefficient as a bifurcating parameter. It is rigorously proved that a branch of nonconstant solution … WebGlobal Bifurcation and Chaos in Gear Model. The study of homoclinic bifurcation that enables predicting the chaotic behaviors of nonlinear systems is well done by the Melnikov theory. The Melnikov method is one of the few analytical methods to study the global bifurcation of the system and gives a procedure for analyzing and estimating when a ...
Global bifurcation and chaos
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WebJun 30, 2006 · Chapter 1. Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems (Pei Yu) Chapter 2. Grazing Flows in Discontinuous Dynamic Systems (Albert C.J. Luo) Chapter 3. Global Bifurcations of … WebMar 14, 2024 · Such a chaotic transient can take very long and therefore, with finite time simulations or measurements, it can be challenging to find out whether a systems really possesses a chaotic attractor (with persistent chaos) or whether we observe “just” transient chaos. Another type of global bifurcation is the interior crisis, where the size of ...
WebApr 12, 2024 · The global oscillation amplitude M as a function of the inactivation ratio p for selected sets of parameters (different coupling strengths K and distances from bifurcation σ) and strategies of placing the oscillators from the oscillatory to the excitable regime, as indicated by different colors. Notably, for smaller distances from bifurcation ... WebBifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in physics and engineering. Each chapter is …
WebThe investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional functions … WebThe global dynamical analysis of an H-bridge parallel resonant converter under a zero current switching control is described in . ... For two-parameter families of special type of generating functions, the bifurcation as well as chaos in the real dynamics is described by author [43, 44]. The description of the real dynamics of transcendental ...
WebAbout this book. Global Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the mechanisms …
WebA bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Topology ... brazier\u0027s ijWebMay 7, 2024 · working area optimization scheme can effectively avoid the homoclinic bifurcation in the PS-HEV during the driving pro-cess and prevent the vehicle from entering the chaotic state. Keywords Electromechanical coupling, global bifurcation, chaos, Melnikov analysis Date received: 7 May 2024; accepted: 5 August 2024 Handling Editor: … brazier\\u0027s ilWebIn this paper a bifurcation analysis of a piecewise-affine discrete-time dynamical system is carried out. Such a system derives from a well-known map which has good features from its circuit implementation point of view and good statistical properties in the generation of pseudo-random sequences. The considered map is a generalization of it and the … brazier\u0027s ilWebApr 10, 2024 · We derive a global Poincaré return map to prove the existence of the double-scroll attractor and explicitly characterize its global dynamical properties. In particular, we demonstrate that the double-scroll attractor corresponds to an attractor of the Poincaré map, which is confined inside four spiral strips lying on two global odd … brazier\\u0027s ikWebPrey and predator birth-rates are treated as bifurcation parameters and the theorems of global bifurcation theory are adapted so that they apply easily to the system. Thus ranges of parameters are found for which there exist nontrivial steady-state solutions. ... 27 August 2024 International Journal of Bifurcation and Chaos, Vol. 29, No. 09 ... brazier\\u0027s imWebJan 1, 2010 · The global bifurcations and chaotic motions are investigated analytically for an arch structure with parametric and forced excitation. The critical curves separating the chaotic and non-chaotic regions are drawn, which show that the system in the case of … t5 virilidadeWebJun 1, 2024 · Based on the Crandall-Rabinowitz bifurcation theory [18], in this section, we provide a strict global bifurcation discussion in the 1D interval Ω = (0, L), L > 0. The user-friendly version of the Crandall-Rabinowitz bifurcation theory was proposed by Shi and Wang [19] in 2009, which implied that the prey-taxis term χ ∇ ( v ∇ u ) can ... brazier\\u0027s ii