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This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals…
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…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given…
We analyse the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the systems dynamic displays excitability by calculating the…
We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann, et al. [Phys. Rev. E {\bf 71}, 051904 (2205)] has…
When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the…
We study the bifurcations and the chaotic behaviour of a periodically forced double-well Duffing oscillator coupled to a single-well Duffing oscillator. Using the amplitude and the frequency of the driving force as control parameters, we…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
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 study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
We derive the normal form for the delay-induced Hopf bifurcation in the first-order phase-locked loop with time delay by the multiple scaling method. The resulting periodic orbit is confirmed by numerical simulations. Further detailed…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…