Related papers: Dynamics of delay-coupled excitable neural systems
The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
We numerically investigate the influence of intrinsic channel noise on the dynamical response of delay-coupling in neuronal systems. The stochastic dynamics of the spiking is modeled within a stochastic modification of the standard…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
Visual illusions provide a window into the mechanisms underlying visual processing, and dynamical neural circuit models offer a natural framework for proposing and testing theories of their emergence. We propose and analyze a delay-coupled…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
We study two coupled systems, one playing the role of the driver system and the other one of the driven system. The driver system is a time-delayed oscillator, and the driven or response system has a negligible delay. Since the driver…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability…
The controllable transition between the Turing and antispiral patterns is studied by using time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as perturbation and analyze the effect of the time delay on the…