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...

We use a bifurcation approach to prove an abstract version of anti-maximum principle. The proof is different from previous approaches.

We study a system of two integrodifferential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By H o p f bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.

E e as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0 > 0; this affirmatively answers conjecture [RCBM, Conjecture 3.12] for such values of the weighted volume parameter. We also prove that the set of weighted volumes such that this characterization holds true is open, thus reducing the proof of the full conjecture to excluding the possibility of bifurca...

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...

One orbit flip and two inclination flips bifurcation is considered with resonant principal eigenvalues. We introduce a local active coordinate system to establish bifurcation equation and obtain the conditions when the original homoclinic orbit is kept or broken. We also prove the existence and the existence regions of double 1-periodic orbit bifurcation. Moreover, the complicated homoclinic-do...

We consider parametrized families of diieomorphisms bifurcating through the creation of critical saddle-node cycles and we show that they exhibit H enon-like strange attractors for a set of parameter values which has positive Lebesgue density at the bifurcation value. This is the rst example of a bifurcation mechanism displaying such prevalence of H enon-like chaotic behaviour. Furthermore, for...

Article history: Received 7 December 2010 Available online 1 October 2011 Submitted by J. Shi

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, ...