Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
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TL;DR: An optimal velocity model which includes the reflex time of drivers is investigated, which finds branches of oscillating solutions connecting Hopf bifurcation points, which may be super- or subcritical, depending on parameters.
Abstract: We investigate an optimal velocity model which includes the reflex time of drivers After an analytical study of the stability and local bifurcations of the steady-state solution, we apply numerical continuation techniques to investigate the global behavior of the system Specifically, we find branches of oscillating solutions connecting Hopf bifurcation points, which may be super- or subcritical, depending on parameters This analysis reveals several regions of multistability
130 citations
TL;DR: Multiple chaotic attractors, implying several independent chaotic attractor generated simultaneously in a system from different initial values, are a very interesting and important nonlinear pheno...
Abstract: Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear pheno
130 citations
TL;DR: In this paper, the authors derived the global structure of the bifurcation diagram for steady-state solutions and studied the behavior of solutions in the limit that short-range repulsive forces are neglected.
Abstract: Under the influence of long-range attractive and short-range repulsive forces, thin liquid films rupture and form complex dewetting patterns. This paper studies this phenomenon in one space dimension within the framework of fourth-order degenerate parabolic equations of lubrication type. We derive the global structure of the bifurcation diagram for steady-state solutions. A stability analysis of the solution branches and numerical simulations suggest coarsening occurs. Furthermore, we study the behaviour of solutions in the limit that short-range repulsive forces are neglected. Both asymptotic analysis and numerical experiments show that this limit can concentrate mass in δ-distributions.
130 citations
TL;DR: In this paper, the authors give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems and present a small number of well-chosen examples of various kinds of nonsmooth systems.
Abstract: The aim of the paper is to give an overview of bifurcation phenomena which are typical for non-smooth dynamical systems. A small number of well-chosen examples of various kinds of non-smooth systems will be presented, followed by a discussion of the bifurcation phenomena in hand and a brief introduction to the mathematical tools which have been developed to study these phenomena. The bifurcations of equilibria in two planar non-smooth continuous systems are analysed by using a generalised Jacobian matrix. A mechanical example of a non-autonomous Filippov system, belonging to the class of differential inclusions, is studied and shows a number of remarkable discontinuous bifurcations of periodic solutions. A generalisation of the Floquet theory is introduced which explains bifurcation phenomena in differential inclusions. Lastly, the dynamics of the Woodpecker Toy is analysed with a one-dimensional Poincare map method. The dynamics is greatly influenced by simultaneous impacts which cause discontinuous bifurcations.
129 citations
TL;DR: In this article, the dynamics of a classical third-order Newton-type iterative method is studied when it is applied to degrees two and three polynomials, and the root-finding method is used to find a bifurcation diagram.
128 citations