Homoclinic and heteroclinic orbits for a semilinear parabolic equation

Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation

This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being f...

Heteroclinic orbits of semilinear parabolic equations

A Survey On Homoclinic And Heteroclinic Orbits

The study of homoclinic and heteroclinic orbits has a long history. This paper surveys some of the recent advances in this topic. We present some of the main results obtained in recent years, and in addition we indicate some possible research directions and some problems for further studies.

On Homoclinic and Heteroclinic Orbits for Hamiltonian Systems

We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach.

Homoclinic and heteroclinic orbits in a modified Lorenz system

This paper presents a mathematically rigorous proof for the existence of chaos in a modified Lorenz system using the theory of Shil’nikov bifurcations of homoclinic and heteroclinic orbits. Together with its dynamical behaviors, which have been extensively studied, the chaotic dynamics of the modified Lorenz system are now much better understood, providing a rigorous theoretic foundation to sup...