منابع مشابه
The Cusp-hopf bifurcation
The coalescence of a Hopf bifurcation with a codimension-two cusp bifurcation of equilibrium points yields a codimension-three bifurcation with rich dynamic behavior. This paper presents a comprehensive study of this cusp-Hopf bifurcation on the three-dimensional center manifold. It is based on truncated normal form equations, which have a phase-shift symmetry yielding a further reduction to a ...
متن کاملUnfolding the Cusp-Cusp Bifurcation of Planar Endomorphisms
Abstract. In many applications of practical interest, for example, in control theory, economics, electronics and neural networks, the dynamics of the system under consideration can be modelled by an endomorphism, which is a discrete smooth map that does not have a uniquely defined inverse; one also speaks simply of a noninvertible map. In contrast to the better known case of a dynamical system ...
متن کاملMultiple attractors via CUSP bifurcation in periodically varying environments
Periodically forced (non-autonomous) single species population models support multiple attractors via tangent bifurcations, where the corresponding autonomous models support single attractors. Elaydi and Sacker obtained conditions for the existence of single attractors in periodically forced discrete-time models. In this paper, the Cusp Bifurcation Theorem is used to provide a general framework...
متن کاملBifurcation of Limit Cycles in a Class of Liénard Systems with a Cusp and Nilpotent Saddle
In this paper the asymptotic expansion of first-order Melnikov function of a heteroclinic loop connecting a cusp and a nilpotent saddle both of order one for a planar near-Hamiltonian system are given. Next, we consider the bifurcation of limit cycles of a class of hyper-elliptic Liénard system with this kind of heteroclinic loop. It is shown that this system can undergo Poincarè bifurcation fr...
متن کاملCusp algebras
By a cusp V we shall mean the image of the unit disk D under a bounded injective holomorphic map h into C whose derivative vanishes at exactly one point. The simplest example is the Neil parabola, given by h(ζ) = (ζ, ζ). See [3, 4] for background and theory on the Neil parabola, which is pictured in Figure 1. A generalization of a cusp is a petal. A petal is the image of the unit disk D under a...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2007
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.1852