Related papers: Sequential noise-induced escapes for oscillatory n…
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…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
Local networks of neurons are nonlinear systems driven by synaptic currents elicited by its own spiking activity and the input received from other brain areas. Synaptic currents are well approximated by correlated Gaussian noise. Besides,…
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…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The…
Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from…
Nonlinear complex network-coupled systems typically have multiple stable equilibrium states. Following perturbations or due to ambient noise, the system is pushed away from its initial equilibrium and, depending on the direction and the…
We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of…
The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
Noise-induced switching between coexisting metastable states occurs in a wide range of far-from-equilibrium systems including micro-mechanical oscillators, epidemiological and climate change models, and nonlinear electronic transport 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…
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…
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state…
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…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…