Related papers: Pitchfork and Hopf bifurcation threshold in stocha…

In this article we study a class of delay differential equations with infinite delay in weighted spaces of uniformly continuous functions. We focus on the integrated semigroup formulation of the problem and so doing we provide an spectral…

Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the…

We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…

In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…

This paper concerns two-dimensional Filippov systems --- ordinary differential equations that are discontinuous on one-dimensional switching manifolds. In the situation that a stable focus transitions to an unstable focus by colliding with…

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of…

We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the critical parameter scaling, when the instability locus propagates…

Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…

We consider boundary value problems for semilinear hyperbolic systems of the type $$ \partial_tu_j + a_j(x,\la)\partial_xu_j + b_j(x,\la,u) = 0, \; x\in(0,1), \;j=1,\dots,n $$ with smooth coefficient functions $a_j$ and $b_j$ such that…

This paper presents a control-oriented delay-based modeling approach for the exponential stabilization of a scalar neutral functional differential equation, which is then applied to the local exponential stabilization of a one-layer neural…

We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space…

There have been significant recent advances in our understanding of the potential use and limitations of early-warning signs for predicting drastic changes, so called critical transitions or tipping points, in dynamical systems. A focus of…

In this paper, we analyze some local stability and local bifurcation properties of the Proportionally fair, TCP fair, and the Delay-based dual algorithms in the presence of two distinct time delays. In particular, our focus is on the…

Since the seminal work by H.L.F. Helmholtz in 1863, to understand the basic principles of hearing has been a great, but still unresolved, challenge for physicists. Some time ago, it has been pointed out (Egu\'{\i}luz et al., Phys. Rev.…

The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via…

For systems of delay differential equations the Hopf bifurcation was investigated by several authors. The problem we consider here is that of the possibility of emergence of a codimension two bifurcation, namely the Bautin bifurcation, for…

This paper introduces a methodology to derive explicit power series approximations for the limit cycle periodic solutions of the Hopf bifurcation in autonomous discrete delay differential equations (DDE). The procedure extends the…

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and…

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…