the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

the present paper deals with a toxin producing phytoplankton (tpp)-zooplankton interaction in spatial environment in thecontext of phytoplankton bloom. in the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. after that tpp-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both popu...

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means center manifold theory. This theory allows isolate complicated asymptotic behavior system close equilibrium point and obtain meaningful predictions its analyzing reduced order on so-called manifold. Since usually not known, good approximation methods are important as...

We define center manifold as usual as an invariant manifold, tangent to the invariant subspace of the linearization of the mapping defining a continuous dynamical system, but the center subspace that we consider is associated with eigenvalues with small but not necessarily zero real parts. We prove existence and smoothness of such center manifold assuming that certain inequalities between the c...