Dynamical behavior of neural ensembles: bifurcation analysis approach

Bifurcation analysis and dynamics of a Lorenz –type dynamical system 

./files/site1/files/0Abstract1.pdfIn this paper we consider a continues Lorenz – type dynamical system. Dynamical behaviors of this system such as computing equilibrium points, different bifurcation curves and computation of normal form coefficient of each bifurcation point analytically and numerically. In particular we derived sufficient conditions for existence of Hopf and Pitchfork bifurcati...

Numerical Bifurcation Analysis of Dynamical Systems

Synchronization of intermittent behavior in ensembles of multistable dynamical systems.

We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the basins of attraction of coexisting synchronous states. Then, we propose the use of the master stability function (MSF) for multistable systems to describe sync...

Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems

This paper is concerned with the relationship between the discount rate and the nature of long-run behavior in dynamic optimization models. The theory is developed under two conditions. The first is history independence, which rules out multiple limit sets. The second is a condition that avoids the reversion to a stable steady state, as the discount factor is lowered, once cycles have emerged. ...

Dynamical behavior and bifurcation analysis of a homogeneous reaction–diffusion Atkinson system

In this paper, we are concerned with a homogeneous reaction–diffusion Atkinson oscillator system subject to homogeneous Neumann boundary conditions on a bounded spatial domain. Using the comparison principle and the techniques of invariant rectangle, we prove the existence of the attraction region of the solutions. We thus prove that under certain conditions, the solutions of the PDE system con...