In this paper we develop an extended center manifold reduction method: a methodology to analyze the formation and bifurcations of small-amplitude patterns in certain classes of multi-component, singularly perturbed systems of partial differential equations. We specifically consider systems with a spatially homogeneous state whose stability spectrum partitions into eigenvalue groups with distinc...

We consider positive, radial and exponentially decaying steady state solutions of the general reaction-diffusion and Klein-Gordon type equations and present an explicit construction of infinite-dimensional invariant manifolds in the vicinity of these solutions. The result is a precise stable manifold theorem for the reaction-diffusion equation and a precise center-stable manifold theorem for th...

The dynamics of a system of two semiconductor lasers, which are delay coupled via a passive relay within the synchronization manifold, are investigated. Depending on the coupling parameters, the system exhibits synchronized Hopf bifurcation and the stability switches as the delay varies. Employing the center manifold theorem and normal form method, an algorithm is derived for determining the Ho...

Using the solution of the center-focus problem from [4], we present the investigation of isochronicity and critical period bifurcations of two families of cubic 3-dim systems of ODEs. Both cubic systems have a center manifold filled with closed trajectories. The presented study is performed using computer algebra systems Mathematica and Singular.

The one dimension computational model of a sequential injection engine, which runs on compressed natural gas (CNG) with spark ignition, is developed for this study, to simulate the performance of gas flow pressure profile, under various speed conditions. The computational model is used to simulate and study of the steady state and transient processes of the intake manifold. The sequential injec...