A large number of simultaneous frequency and amplitude data from an electronic chaotic circuit (Chua’s circuit) have been obtained. These acquisitions are validated by plotting the bifurcation diagrams of the experimental data versus the bifurcation parameter. We introduce a topological parallel between the Colpitts oscillator and Chua’s circuit, and look for similar behavior of the frequency f...

The existence of positive equilibrium solutions to age-dependent population equations with nonlinear diffusion is studied in an abstract setting. By introducing a bifurcation parameter measuring the intensity of the fertility it is shown that a branch of (positive) equilibria bifurcates from the trivial equilibrium. In some cases the direction of bifurcation is analyzed.

A continuous dynamical system is presented in which the period -adding phenomenon is observed when a bifurcation parameter is changed . This phenomenon is characterized by a family of onedimensional return maps of a cusp shape which exhibits a saddle-node bifurcation .

We show that in a reaction diffusion system on a two-dimensional substrate with advection in the confined direction, the drift (advection) induced instability occurs through a Hopf bifurcation, which can become a double Hopf bifurcation. The box size in the direction of the drift is a vital parameter. Our analysis involves reduction to a low dimensional dynamical system and constructing amplitu...

The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko’s conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve.

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing t...

A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before an...

Abstract—The Nagumo-Sato model is one of mathematical neuron models described by a piecewise linear difference equation. Since there is a conditional character which is discontinuous at the threshold value, the system can be classified as a hybrid dynamical system. Bifurcation phenomena are occurred by changing internal parameters and chaotic attractors are also given. The dynamical properties ...

This paper focuses on Hopf bifurcation control in a dual model of Internet congestion control algorithms which is modeled as a delay differential equation (DDE). By choosing communication delay as a bifurcation parameter, it has been demonstrated that the system loses stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Therefore, a time-delayed feed...

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...