Existence of Heteroclinic Orbits for Systems Satisfying Monotonicity Conditions
نویسندگان
چکیده
We prove existence of heteroclinic orbits for systems of ordinary differential equations satisfying monotonicity conditions. The proof is carried out by means of the implicit function theorem. We apply these results to prove existence of travelling waves for the system describing a multicomponent plasma sustained by a laser beam.
منابع مشابه
Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems
This paper presents the existence of Si'lnikov orbits in two different chaotic systems belong to the class of Lorenz systems, more exactly in the Lu system and in the Zhou's system. Both systems have exactly two heteroclinic orbits which are symmetrical with respect to the z-axis by using the undetermined coefficient method. The existence of the homoclinic orbit for the Zhou's system has been p...
متن کاملSingular Perturbation Theory for Homoclinic Orbits in a Class of Near-Integrable Dissipative Systems
This paper presents a new unified theory of orbits homoclinic to resonance bands in a class of near-integrable dissipative systems. It describes three sets of conditions, each of which implies the existence of homoclinic or heteroclinic orbits that connect equilibria or periodic orbits in a resonance band. These homoclinic and heteroclinic orbits are born under a given small dissipative perturb...
متن کاملOn the existence of non-horseshoe-type chaos in 3-D quadratic continuous-time systems
In this paper, we obtain non-existence conditions for horseshoetype chaos in 3-D quadratic continuous-time systems. This kind of chaos in polynomial ODE systems is characterized by the non-existence of homoclinic and heteroclinic orbits.
متن کاملSymmetric periodic orbits near a heteroclinic loop
In this paper we consider vector fields in R that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e and e−) and their invariant manifolds: one of dimension 2 (a sphere minus the points e and e−) and one of dimension 1 (the open diameter of the sphere having endpoints e and e−). In particular, we analyze the dynamics of t...
متن کاملTransition Layers for Singularly Perturbed Delay Differential Equations with Monotone Nonlinearities
Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heter...
متن کامل