A hybrid system approach is adopted to study the dynamic behaviour of a controlled reverse flow reactor in which a feedback control law dictates the occurrence of flow inversions. Typical behaviour of hybrid systems (Zeno phenomena) are found coexisting with other regimes like limit cycles and quasi-periodic regimes. Construction of impact maps, continuation of limit cycles and detection of loc...

We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that-after a saddle node bifurcation of limit cycles-the full model dynamics temporarily follow a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical ap...

A class of polynomial systems of odd degree with limit cycles, invariant parabolas and invariant straight lines, is examined. The limit cycles can be obtain as a bifurcation of a non hyperbolic focus at the origin as Hopf bifurcations. We will also obtain the necessary and sufficient conditions for the critical point at the interior of bounded region to be a center. 2010 Mathematics Subject Cla...

In this paper we study the existence, number and distribution of limit cycles of the perturbed Hamiltonian system: 0960-0 doi:10 E-m x0 1⁄4 4yðabx by þ 1Þ þ ex ux þ vy b þ 1 l þ 1 x y ux k y0 1⁄4 4xðax aby 1Þ þ eyðux þ vy þ bxy vy kÞ where l + b = n, 0 < a < b < 1, 0 < e 1, u, v, k are the real parameters and n = 2k, k an integer positive. Applying the Abelian integral method [Blows TR, Perko L...

cl matcont and matcont are matlab continuation packages for the interactive numerical study of a range of parameterized nonlinear dynamical systems, in particular ODEs. matcont is an interactive graphical package and cl matcont is a commandline version. Both packages allow to compute curves of equilibria, limit points, Hopf points, limit cycles, flip, fold and torus bifurcation points of limit ...