Existence and stability of traveling waves in parabolic systems of differential equations with weak diffusion

The aim of the present paper is to investigate some properties periodic solutions a nonlinear autonomous parabolic systems with condition. We differential equations using an integral manifolds method theory oscillations. prove existence in system weak diffusion on circle. study and stability arbitrarily large finite number cycles for diffusion. solution equation sought form traveling wave. A representation manifold obtained. seek condition Fourier series complex introduce norm space coefficients expansion. use normal forms general retarded argument bifurcation delay quasilinear equations. circle small proved. problems waves are investigated.