Bifurcation of heteroclinic orbits via an index theory

An Equivariant, Inclination-flip, Heteroclinic Bifurcation

We examine a heteroclinic bifurcation occurring in families of equivariant vector elds. Within these families, the ows contain structurally stable heteroclinic cycles. The ow can twist around the cycle to produce what is the equivalent of an \inclination-ip" homoclinic orbit. An unfolding of this bifurcation in a generic one-parameter equivariant family shows that Smale horseshoes are embedded ...

Heteroclinic orbits of semilinear parabolic equations

Heteroclinic Orbits for Retarded Functional Differential Equations*

Suppose r is a heteroclinic orbit of a Ck functional differential equation i(t) =f(x,) with a-limit set a(T) and o-limit set w(T) being either hyperbolic equilibrium points or periodic orbits. Necessary and sufficient conditions are given for the existence of an 7 close to f in Ck with the property that i(t) = 3(x,) has a heteroclinic orbit p close to f. The orbits p are obtained from the zeros...

Dissipation-Induced Heteroclinic Orbits in Tippe Tops

This paper demontrates that the conditions for the existence of a dissipation-induced heteroclinic orbit between the inverted and noninverted states of a tippe top are determined by a complex version of the equations for a simple harmonic oscillator: the modified Maxwell– Bloch equations. A standard linear analysis reveals that the modified Maxwell–Bloch equations describe the spectral instabil...

Heteroclinic orbits Arising from Coupled Chua's Circuits

Chua’s circuit is a simple electronic circuit exhibiting a wide variety of bifurcation and chaotic phenomena. Because of its universality and simplicity, Chua’s circuit has captured much interest among researchers in science and engineering. The circuit equations are described by the following set of differential equations: C1 dVC1 dt = 1 R (VC2 − VC1) − F (VC1) , C2 dVC2 dt = 1 R (VC1 − VC2) +...