Noise-controlled bistability in an excitable system with positive feedback

Abstract

-We study the interplay between noise and a positive feedback mechanism in an excitable system that generates events. We show that such a system can exhibit a bistability in the dynamics of the event generation (states of low and high activity). The stability of the two states is determined by the strength of the noise such that a change of noise intensity permits complete control over the probabilities with which the two states are occupied. The bistability also has strong implications for the regularity of the event generation. While the irregularity of the interevent interval (short-time variability) and of the asymptotic Fano factor of the event count (long-time variability) is limited if the system is only in one of the two states, we show that both measures of variability display giant values if both states are equally likely. The long-time variability is additionally amplified by long-range positive correlations of the interevent intervals.Introduction. -Excitable systems that generate allorx-none responses -or, generally speaking, events -are ubiquitous. Prominent examples are the action potentials of nerve cells [1], concentration pulses of intracellular calcium [2], dropout events of lasing intensity in excitable lasers with optical feedback [3], and blackouts of the power supply [4], to name but a few. Excitability can only occur in systems that are far from thermodynamic equilibrium and is often accompanied by a considerable amount of fluctuations [5,6]. This is particularly interesting from a theoretical point of view because the interaction of noise and the inherently nonlinear mechanism of excitability leads to nontrivial effects such as the well-studied phenomena of stochastic resonance and coherence resonance [5,7].

Noise-induced transitions in a double-well excitable oscillator

“…[26,27]). Noise-induced transitions were observed in excitable systems ranging from a single excitable neuron [28][29][30] to coupled excitable elements and media [31,32]. In many cases noise-induced transitions are not true bifurcations [33], rather they underlie qualitative changes of the stochastic dynamics.…”

Delay-induced stochastic bursting in excitable noisy systems

“…[13,14]. We will show that a small additional delayed feedback (large feedback can significantly modify the dynamics, see, e.g., [15]) leads to an interesting partially coherent spike pattern which we call stochastic bursting. Bursting describes a general phenomenon with quiescent periods following periods of rapid repeated firing and is thought to be important in communication between neurons and synchronization [16].…”

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

“…Moreover, in recent years, several theoretical investigations have focused on the positive effects of the noise on nonlinear systems, showing that, under suitable conditions, the addition of external fluctuations to intrinsically noisy systems may induce an enahncement of the dynamical stability of the system, resulting in a less noisy response [18][19][20][21][22][23][24][25][26][27][28]. This counterintuitive effect has been found in different physical areas, ranging from the generation of spin currents [29], aggregation kinetics of Brownian particles [30,31], chemical reaction system [32], translocation dynamics of polymers [33][34][35], ultra-fast magnetization dynamics of magnetic spin systems [36,37], dynamic electron response in zinc-blende semiconductor crystals [38][39][40][41][42][43], noise redistribution in quasi 2D Silicon Mos inversion layers [44], to interdisciplinary physical models [45][46][47][48][49][50][51][52].…”