In this paper, dynamical analysis is presented for a group of unicycles in leader-follower formation. The equilibrium formations were characterized along with the local stability analysis. It was demonstrated that with the variation in control gain, the collective dynamics might undergo Andronov-Hopf and Fold-Hopf bifurcations. An increase in the number of unicycles increase the vigor of quasi-...

For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the...

In this paper we investigate the dynamics associated with a degenerate codimension two Takens-Bogdanov bifurcation which arises in a recently derived model for selfexciting dynamo action introduced by Hide et al. [1]. The general unfolding of such a codimension three bifurcation has already been discussed in an abstract setting by Li and Rousseau [4]. Here we describe the unfolding scenario in ...

The present work will focus on a Kaldor-Kalecki non –linear business cycle model in income and capital, with discrete time and delay argument characteristics. What it will state, considering an investment function similar to the one proposed by Rodano and using the linear approximation analysis, are the local stability property and local bifurcations conditions, given the parameter space. Numer...