In this paper, a nonlinear business cycle model of Kaldor-type with delay is considered. A Hopf bifurcation is proved to occur as the delay (taken as a parameter of bifurcation) crosses some critical value. Mathematics Subject Classification: 34K18, 91B62

We prove that the study of Rimmer bifurcation of symmetric fixed points in two–dimensional discrete reversible dynamical systems can be achieved analysing either bifurcation of critical points of a symmetric Hamiltonian function or the bifurcation of symmetric equilibrium points for a nonconservative reversible vector field. We give the normal forms for generating functions of area preserving r...

We consider a ring of identical elements with time delayed, nearest-neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The bifurcation and stability of nontrivial asynchronous oscillations from the trivial solution are analysed using equivariant bifurcation theory and centre manifold constr...

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...

We are concerned with an activator-inhibitor system on an n-dimensional ball such that the inhibitor is activated by an activator as well as the spatial average of its inhibitor. We analyze the existence of the radially symmetric solutions and the occurrence of Hopf bifurcation in the interfacial problem as the bifurcation parameters vary. Mathematics Subject Classification: 35R35, 35B32, 35B25...