Related papers: Noise Induced Switching and Extinction in Systems …
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
A dynamical system is said to undergo rate-induced tipping when it fails to track its quasi-equilibrium state due to an above-critical-rate change of system parameters. We study a prototypical model for rate-induced tipping, the saddle-node…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…
Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity…
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
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…
Species populations often modify their environment as they grow. When environmental feedback operates more slowly than population growth, the system can undergo boom-bust dynamics, where the population overshoots its carrying capacity and…
We demonstrate the possibility to systematically steer the most probable escape paths (MPEPs) by adjusting relative noise intensities in dynamical systems that exhibit noise-induced escape from a metastable point via a saddle point. Using a…
The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that…
We consider the effect of Gaussian white noise on fast-slow dynamical systems with one fast and two slow variables, containing a folded-node singularity. In the absence of noise, these systems are known to display mixed-mode oscillations,…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
We analyze a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time (stochastic difference equations), continuous…