A simplified model of a container crane subject to a delayed feedback is investigated. The conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined. It is shown that a subcritical Hopf bifurcation to unstable oscillations cannot be ruled out and the undesired coexistence of stable large amplitude oscillations and a stable equilibrium endangers the robustness of ...

Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of information and the transmission machinery induce communication delays, due to the transport of information (propagation delays) and to the synaptic machinery (constant delays). We investigate the role of these delays...

Rapid and dramatic changes in climate and glacial conditions have taken place during the last 2.5 million years of the earth’s history. Huge ice sheets expanded and contracted periodically, at times covering large areas of North America and Europe. Global sea levels dropped and rose 100 m to 150 m in response to the growth and melting of glaciers, causing continental coast lines to move far int...

Using spatial dynamics, we prove a Hopf bifurcation theorem for viscous Lax shocks in viscous conservation laws. The bifurcating viscous shocks are unique (up to time and space translation), exponentially localized in space, periodic in time, and their speed satisfies the Rankine–Hugoniot condition. We also prove an ”exchange of spectral stability” result for superand subcritical bifurcations, ...

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 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, a five-neuron bidirectional associative memory (BAM) neural network with two time delays is studied. Since the study of Hopf bifurcation is very important for the design and application of BAM neural networks, we investigate that Hopf bifurcation occurs and a family of periodic solutions appear when the sum of two delays passes through a critical value.

We investigate Hopf bifurcations in a delayed Nicholson’s blowflies equation of neutral type, derived from the Gurtin–MacCamy model. A key parameter that determines the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Global extension of local Hopf branches is established by combining a global Hopf bifurcation theorem with a Bendixson criteri...

The diffusive Lotka–Volterra predator–prey system with two delays is reconsidered here. The stability of the coexistence equilibrium and associated Hopf bifurcation are investigated by analyzing the characteristic equations, and our results complement earlier ones. We also obtain that in a special case, a Hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system. © 2011 ...

In this paper we study the Hopf bifurcation for the tumor-immune system model with one delay. This model is governed by a system of two differential equations with one delay. We show that the system may have periodic solutions for small and large delays for some critical value of the delay parameter via Hopf bifurcation theorem bifurcating from the non trivial steady state.