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Motivated by the theory of reaction kinetics based on nonequilibrium thermodynamics and the linear stability of driven reaction-diffusion, we apply the Fokker-Planck equation to describe the population dynamics of an ensemble of reactive…
We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and…
We study the dynamics of multipulse solutions in mode-locked lasers in presence of time-delayed feedback stemming, e.g., from reflections upon optical elements, and carrier dynamics. We demonstrate that the dynamics of such a high…
Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics…
We theoretically investigate the effect of dissipation on multi-photon excitation of Rydberg atoms. The steady states and the dynamics are compared via two types of four-level excitation schemes with different dissipative paths of…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
This paper explores the classification of parameter spaces for reaction-diffusion systems of two chemical species on stationary domains. The dynamics of the system are explored both in the absence and presence of diffusion. The parameter…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
Systems of coupled sine circle maps show regimes of spatiotemporally intermittent behaviour with associated scaling exponents which belong to the DP class, as well as regimes of spatially intermittent behaviour (with associated regular…
We study the dynamics of a reaction-diffusion system composed of two mutually coupled excitable fibers. We focus on the situation in which dynamical properties of the two fibers are not identical because of the parameter difference between…
Spontaneous rhythmic oscillations are widely observed in various real-world systems. In particular, biological rhythms, which typically arise via synchronization of many self-oscillatory cells, often play important functional roles in…
The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential is studied. It is shown that if the pair potential allows for a discontinuous reduction of the…
In this paper we analyze a generic dynamical system with $\mathbb{D}_2$ constructed via a Cayley graph. We study the Hopf bifurcation and find conditions for obtaining a unique branch of periodic solutions. Our main result comes from…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting system within which multitudes of different sizes of large scale coherent structures emerge, resulting in a globally nonlinear stochastic behavior vastly different…
The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, that allows to calculate explicitly the dynamic properties of the system, is developed. It is shown that…
We investigate the relative phase coherence properties and the occurrence of demixing instabilities for two mutually interacting and time evolving Bose-Einstein condensates in traps. Our treatment naturally includes the additional…
Stochasticity plays important roles in reaction systems. Vector fields of probability flux and velocity characterize time-varying and steady-state properties of these systems, including high probability paths, barriers, checkpoints among…
The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a…
Phase separation plays a central role in the emergence of novel functionalities of correlated electron materials. The structure of the mixed-phase states depends strongly on the nonequilibrium phase-separation dynamics, which has so far yet…