The dynamic behaviour of a Lotka-Volterra system, described by a planar map, is analytically and numerically investigated. We derive analytical conditions for stability and bifurcation of the fixed points of the system and compute analytically the normal form coefficients for the codimension 1 bifurcation points flip and Neimark-Sacker , and so establish subor supercriticality of these bifurcat...

A simple method to follow the postbuckling paths in the finite element analysis is presented. During a standard path-following by means of arc-length method, the signs of diagonal elements in the triangularized tangent stiffness matrix are monitored to determine the existence of singular points between two adjacent solution points on paths. A simple approach to identify limit or bifurcation poi...

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 investigate the behaviour of a neural network model consisting of three neurons with delayed self and nearest-neighbour connections. We give analytical results on the existence, stability and bifurcation of nontrivial equilibria of the system. We show the existence of codimension two bifurcation points involving both standard and D3-equivariant, Hopf and pitchfork bifurcation points. We use ...