Related papers: A primer on noise-induced transitions in applied d…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
The dynamics of populations is frequently subject to intrinsic noise. At the same time unknown interaction networks or rate constants can present quenched uncertainty. Existing approaches often involve repeated sampling of the quenched…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
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…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major…
To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the…
We present a comprehensive study of the phase transitions in the single-field reaction-diffusion stochastic systems with field-dependent mobility of a power-low form and the internal fluctuations. Using variational principles and mean-field…
We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a…
Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…
A control strategy is employed that modifies the stochastic escape times from one basin of attraction to another in a model of a double-gyre flow. The system studied captures the behavior of a large class of fluid flows that circulate and…
Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidence appears in favor of event-driven control hypothesis: human…