Related papers: Delay Induced Instabilities in Self-Propelling Swa…
Self-propelled active particles exhibit delayed responses to environmental changes, modulating their propulsion speed through intrinsic sensing and feedback mechanisms. This adaptive behavior fundamentally determines their dynamics and…
In this paper, we show the existence of Hopf bifurcation of a delayed single population model with patch structure. The effect of the dispersal rate on the Hopf bifurcation is considered. Especially, if each patch is favorable for the…
Computational models of collective behavior in birds has allowed us to infer interaction rules directly from experimental data. Using a generic form of these rules we explore the collective behavior and emergent dynamics of a simulated…
Collective motions emerging from the interaction of autonomous mobile individuals play a key role in many phenomena, from the growth of bacterial colonies to the coordination of robotic swarms. For these collective behaviours to take hold,…
The phenomenon of delay-induced resonance implies that in a nonlinear system a time-delay term may be used as an effective enhancer of the oscillations caused by an external forcing maintaining the same frequency. This is possible for the…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in…
The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…
In this article is shown that large systems endowing phase coexistence display self-oscillations in presence of linear feedback between the control and order parameters, where an Andronov-Hopf bifurcation takes over the phase transition.…
We investigate the emergence of a collective periodic behavior in a frustrated network of interacting diffusions. Particles are divided into two communities depending on their mutual couplings. On the one hand, both intra-population…
We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…
We analyze Cucker-Smale flocking particles with delayed coupling, where different constant delays are considered between particles. By constructing a system of dissipative differential inequalities together with a continuity argument, we…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
{We study a model of small-amplitude traveling waves arising in a supercritical Hopf-bifurcation, that are coupled to a slowly varying, real field. The field is advected by the waves and, in turn, affects their stability via a coupling to…
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence…
The motion of self-propelled massive particles through a gaseous medium is dominated by inertial effects. Examples include vibrated granulates, activated complex plasmas and flying insects. However, inertia is usually neglected in standard…