Related papers: Asymptotic methods for stochastic dynamical system…
The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape…
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and…
With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of…
The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
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…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy…
A theoretical approach for characterising the influence of asymmetry of noise distribution on the escape rate of a multi-stable system is presented. This was carried out via the estimation of an action, which is defined as an exponential…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…
We study the exit problem of solutions of the stochastic differential equation dX(t)=-U'(X(t))dt+epsilon dL(t) from bounded or unbounded intervals which contain the unique asymptotically stable critical point of the deterministic dynamical…
We analyze a specific class of random systems that are driven by a symmetric L\'{e}vy stable noise. In view of the L\'{e}vy noise sensitivity to the confining "potential landscape" where jumps take place (in other words, to environmental…
Recently, extracting data-driven governing laws of dynamical systems through deep learning frameworks has gained a lot of attention in various fields. Moreover, a growing amount of research work tends to transfer deterministic dynamical…
A goal of data assimilation is to infer stochastic dynamical behaviors with available observations. We consider transition phenomena between metastable states for a stochastic system with (non-Gaussian) $\alpha-$stable L\'evy noise. With…
Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems…