This paper presents a new steady periodic gait in the compass model. It is proved that the model has period-four gait and the new gait lead to chaos through perioddoubling bifurcation. This paper confirms the existence of the new gait and its bifurcation through the calculation by computer.

The present paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters. The goal of the paper is to formulate this problem and to present some preliminary results.

Standard bifurcation theory is concerned with families of vector fields

My parents, my sister and all my friends who helped me and prayed for me throughout the work on my thesis My God and heavenly father for never leaving me alone, for the love and patience He granted me The Rector of my congregation in Rabenau-Kesselbach and all my brothers and sisters for their prayers The Konrad-Adenauer-Foundation which granted a Ph.D.-scholarship for three years and supported...

We consider a model based on the thermal spike concept for an explanation of latent track formation in YBa2Cu3O7−x single crystal. The model demonstrates some interesting peculiarities such as ®electronic quenching ̄ and existence of bifurcation points. Arguments why the energy spent on damage creation in the track should be equal to melting heat and why the so-called ®epitaxial regrowth ̄ is imp...

We study the global Hopf bifurcation of periodic solutions for one-parameter systems of state-dependent delay differential equations, and specifically we obtain a priori estimates of the periods in terms of certain values of the state-dependent delay along continua of periodic solutions in the Fuller space C(R;RN+1) × R2. We present an example of three-dimensional state-dependent delay differen...

In this paper, we generalize all the existing results in the current literature for the upper bound of a general 3-D quadratic continuoustime system. In particular, we find large regions in the bifurcation parameters space of this system where it is bounded.

For a class of two-point boundary value problems we prove exactness of S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like e for a > 0.

An asymptotically linear elliptic equation on the half-line is considered. A global branch of positive solutions bifurcating from infinity is obtained. Classical global bifurcation theory cannot be applied due to the unboundedness of the domain and recent developments of degree theory are used to prove bifurcation.

This article concerns a symmetrical Lotka-Volterra predator-prey system with delays. By analyzing the associated characteristic equation of the original system at the positive equilibrium and choosing the delay as the bifurcation parameter, the local stability and Hopf bifurcation of the system are investigated. Using the normal form theory, we also establish the direction and stability of the ...