In this paper we study bifurcations in predator-prey systems with seasonal prey harvesting. First, when the seasonal harvesting reduces to constant yield, it is shown that various kinds of bifurcations, including saddle-node bifurcation, degenerate Hopf bifurcation, and Bogdanov– Takens bifurcation (i.e., cusp bifurcation of codimension 2), occur in the model as parameters vary. The existence o...

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a g...

A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the s...

The transition from a two-dimensional to three-dimensional flow in systems with spatial O(2) symmetry and spatiotemporal Z(2) symmetry happens in many fluid systems, like wakes or periodically forced flows. In most of these systems, the dynamics after the first bifurcation is very complex and involves cascades of bifurcations in a very narrow parameter range. A numerical study of a flow in an e...

As an alternative to symbolic differentiation (SD) and finite differences (FD) for computing partial derivatives, we have implemented algorithmic differentiation (AD) techniques into the M bifurcation software C MM, http://sourceforge.net/projects/matcont, where we need to compute derivatives of an iterated map, with respect to state variables. We use derivatives up to the fifth ord...

A regular network is a network with one kind of node and one kind of coupling. We show that a codimension one bifurcation from a synchronous equilibrium in a regular network is at linear level isomorphic to a generalized eigenspace of the adjacency matrix of the network, at least when the dimension of the internal dynamics of each node is greater than 1. We also introduce the notion of a produc...

We apply periodic orbit theory to a two-dimensional nonintegrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shel...

The bursting discharge behaviour of neurons is affected by many factors, among which temperature one the more important factors. In this work, we study and dynamics process two different temperature-sensitive ion channels, potassium current calcium current. case current, waveforms, codimension-1 bifurcations trajectory plots at temperatures indicate that five types (Hopf/Flip, Hopf/Homoclinic, ...

This study aims to provide a better understanding of recently identified transition scenarios exhibited by traveling wave solutions in pipe flow. This particular family of solutions are invariant under certain reflectional symmetry transformations and they emerge from saddle-node bifurcations within a two-dimensional parameter space characterized by the length of the pipe and the Reynolds numbe...

A mathematical model of convection of a Boussinesq fluid in a rotating spherical shell is analyzed using numerical computations guided by bifurcation theory. The fluid is differentially heated on its inner spherical surface, with the temperature increasing from both poles to a maximum at the equator. The model is assumed to be both rotationally symmetric about the polar axis and reflectionally ...