The set of the equations governing the flow model are transformed into differential equations by approximations prior to pursuing the analytical solutions for particle paths. The methodology of dynamical systems
Synonyms Numerical continuation ; Parameter studies ; Path-following ; Qualitative analysis Definition Bifurcation theory refers to the study of qualitative changes to the state of a system as a parameter is varied. It can be applied to steady state systems, or to dynamical systems and can be ...
Section “Mathematical analysis” provides the mathematical elucidation of the proposed model. Section “Bifurcation analysis” delivers the stability and their phase portrait using bifurcation theory. Section “Analytic optical soliton solution” employs the PE and US methodologies to derive optical soliton...
Nonlinear studies of laser systems contributed to the field of dynamical systems with general phenomena including chaos, (chaotic) synchronization of coupled oscillators, competition, excitability, delay-induced instabilities, unfolding of high-codimension bifurcations, bifurcation cascades, and spatial patterns...
modulation of couplings “within” each subnetwork resulted in different global network dynamics, similar to the behavior of GLV equations. However, a systematic analysis of the effect of couplings “between” subnetworks, and therefore a topological dynamical equivalence between GLV systems and the col...
The bifurcation diagram is a graphical tool that is utilized to describe the stability and nonlinear behavior of dynamical systems, difference equations, and differential equations. From: Engineering Failure Analysis, 2024 About this pageSet alert Also in subject area: Computer ScienceDiscover other topi...
The payoff matrix parameters, bifurcation, topological conjugacy and symbolic dynamics of the evolutionary game dynamical systems on a one-dimensional regular lattice are thoroughly investigated in this paper. Based on the properties of addition and scalar multiplication invariance, an effective ...
Dynamical Systems & Nonlinear Phenomena Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents Nonlinear excitations and dynamic features of dust ion-acoustic waves in a magnetized electron–positron–ion plasma Bifurcation analysis in a predator–prey...
(1998). Topological analysis of chaotic dynamical systems.Reviews of Modern Physics,70(4), 1455. 发布于 2023-09-26 19:50 赞同5添加评论 分享收藏喜欢收起liu ren quant 关注 31 人赞同了该回答 分岔是稳态的数目变多,混沌是多到一塌糊涂。混沌来自分岔,分岔不一定混沌。
6. 123 Bifurcation analysis of a forced delay equation for... 2967 Fig. 6 Bifurcation diagram 5.1 Phase plane and phase portraits To illustrate the dynamical behavior of the system, we chose the following angular frequencies of the forcing ωI = 1, ωI I I = 1.005, ωV = 1.013, ωV...