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We analyze the stability of the Rate Control Protocol (RCP) using two different models that have been proposed in literature. Our objective is to better understand the impact of the protocol parameters and the effect different forms of…
Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general…
We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two…
A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…
We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are…
We consider a dynamical system undergoing a saddle-node bifurcation with an explicitly time dependent parameter~$p(t)$. The combined dynamics can be considered as a dynamical systems where $p$ is a slowly evolving parameter. Here, we…
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…
With rising global temperatures Earth's tipping elements are becoming increasingly more vulnerable to crossing their critical thresholds. The reaching of such tipping points does not only impact other tipping elements through their…
This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution…
We show how coupling an ensemble of bistable systems to a common cavity field affects the collective stochastic behavior of this ensemble. In particular, the cavity provides an effective interaction between the systems, and parametrically…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
Humans interact with each other on a daily basis by developing and maintaining various social norms and it is critical to form a deeper understanding of how such norms develop, how they change, and how fast they change. In this work, we…
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…
The use of critical slowing down as an early warning indicator for regime switching in observations from stochastic environments and noisy dynamical models has been widely studied and implemented in recent years. Some systems, however, have…
A variety of real world and experimental systems can display a drastic regime shift, as the evolution in one its paramaters crosses a threshold value. Assimilation of such a transition with a bifurcation has allowed to identify so called…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of…
The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…