this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

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 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 ...

Following Almgren’s construction of the center manifold in his Big regularity paper, we show the C regularity of area-minimizing currents in the neighborhood of points of density one, without using the nonparametric theory. This study is intended as a first step towards the understanding of Almgren’s construction in its full generality. 0. Introduction In this note we consider area-minimizing i...

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...