Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons

We study nontrivial effects of noise on synchronization and coherence of a chaotic Hodgkin-Huxley model of thermally sensitive neurons. We demonstrate that identical neurons which are not coupled but subjected to a common fluctuating input (Gaussian noise) can achieve complete synchronization when the noise amplitude is larger than a threshold. For nonidentical neurons, noise can induce phase synchronization. Noise enhances synchronization of weakly coupled neurons. We also find that noise enhances the coherence of the spike trains. A saddle point embedded in the chaotic attractor is responsible for these nontrivial noise-induced effects. Relevance of our results to biological information processing is discussed.     

Noise-induced transitions in a double-well potential at low friction

A new integral representation of the transition rate holds for any friction and is shown to allow a feasible evaluation in a wide friction range. Analytic approximations include the (high-friction) Kramers result with the leading correction, as well as a low-friction case. The method is complementary to a recent one of Melnikov and Meshkov.     

Noise-induced phase synchronization and synchronization transitions in chaotic oscillators

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.     

Noise-induced synchronization in bidirectionally coupled type-I neurons

We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical value of noise strength that has a clear functional dependence on neuronal coupling strength and input values. For an inhibitory-excitatory (IE) synaptic coupling, the approach to a partially synchronized state is shown to vary qualitatively depending on whether the input is less or more than a critical value. We find that introduction of noise can cause a delay in the bifurcation of the firing pattern of the excitatory neuron for IE coupling.     

Noise-induced optical bistability and state transitions in spin-crossover solids with delayed feedback

Considering the time-delayed feedback and environmental perturbations in spin-crossover system, we construct a stochastic delayed differential equation to study the state transitions from the low spin (LS) state to the high spin (HS) state in spin-crossover solids. It is shown that the delayed feedback and noise can induce optical bistability and state transitions. The mean first-passage time (MFPT) of the transition from the LS state to the HS state as the function of the noise intensity exhibits a maximum, and the noise-enhanced stability is observed. However the MFPT decreases with increase of the delayed feedback intensity, thus the delayed feedback accelerates the conversion from the LS state to the HS state.     

Noise-induced extinction in Bazykin-Berezovskaya population model

A nonlinear Bazykin-Berezovskaya prey-predator model under the influence of parametric stochastic forcing is considered. Due to Allee effect, this conceptual population model even in the deterministic case demonstrates both local and global bifurcations with the change of predator mortality. It is shown that random noise can transform system dynamics from the regime of coexistence, in equilibrium or periodic modes, to the extinction of both species. Geometry of attractors and separatrices, dividing basins of attraction, plays an important role in understanding the probabilistic mechanisms of these stochastic phenomena. Parametric analysis of noise-induced extinction is carried out on the base of the direct numerical simulation and new analytical stochastic sensitivity functions technique taking into account the arrangement of attractors and separatrices.     

Noise-induced current reversal in a stochastically driven dissipative tight-binding model

The cooperative effects induced by external random dichotomic and d.c. driving are studied for charge drift and diffusion in a one-dimensional dissipative tight-binding model. For a strongly correlated dichotomic field the effect of large diffusion acceleration is demonstrated. Additionally, it is shown that the averaged current direction can be inverted by applying a strongly correlated electric field (noise-induced negative conductivity).     

Noise-induced intermittency of a reflexive model with symmetry-induced equilibrium manifold

We discuss a route to intermittency based on the concept of reflexivity, namely on the interaction between observer and stochastic reality. A simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1/f$1/f$-noise. In the absence of noise the model yields a symmetry-induced equilibrium manifold with two stable states. Noise makes this equilibrium manifold unstable, with an escape rate becoming lower and lower upon time increase, thereby generating an inverse power law distribution of waiting times. The distribution of the times of permanence in the basin of attraction of the equilibrium manifold are analytically predicted through the adoption of a first-passage time technique. Finally we discuss the possible extension of our approach to deal with the intermittency of complex systems in different fields.     

Noise-induced generation of saw-tooth type transitions between climate attractors and stochastic excitability of paleoclimate

Motivated by important paleoclimate applications we study a three dimensional model ofthe Quaternary climatic variations in the presence of stochastic forcing. It is shown thatthe deterministic system exhibits a limit cycle and two stable system equilibria. Wedemonstrate that the closer paleoclimate system to its bifurcation points (lying either inits monostable or bistable zone) the smaller noise generates small or large amplitudestochastic oscillations, respectively. In the bistable zone with two stable equilibria,noise induces a complex multimodal stochastic regime with intermittency of small and largeamplitude stochastic fluctuations. In the monostable zone, the small amplitude stochasticoscillations localized in the vicinity of unstable equilibrium appear along with the largeamplitude oscillations near the stable limit cycle. For the analysis of thesenoise-induced effects, we develop the stochastic sensitivity technique and use theMahalanobis metric in the three-dimensional case. To approximate the distribution ofrandom trajectories in Poincare sections, we use a method of confidence ellipses. Aspatial configuration of these ellipses is defined by the stochastic sensitivity and noiseintensity. The glaciation/deglaciation transitions going between two polar Earth’s stateswith the warm and cold climate become easier and quicker with increasing the noiseintensity. Our stochastic analysis demonstrates a near 100 ky saw-tooth type climate selffluctuations known from paleoclimate records. In addition, the enhancement of noiseintensity blurs the sharp climate cycles and reduces the glaciation-deglaciation periodsof the Earth’s paleoclimate.     

Noise-induced hearing damage caused by metabolic exhaustion: a mathematical model

A mathematical model for noise-induced hearing loss is based on the assumption that hair cells are damaged, temporarily or permanently, by metabolic exhaustion, and that the number of damaged hair cells and the hearing loss are monotonically increasing functions of an energy deficiency. The purpose of the model is to focus on the influence of sound intensity, exposure duration, and temporal pattern of the sound exposure on the noise-induced hearing loss from long-duration exposures. The model is restricted to the range of sound levels where metabolic exhaustion probably is the main reason for the hair cell damage. Only exposures with similar frequency spectra and producing moderate hearing losses are considered; frequency dependence is not discussed.     

The geometrical phase transitions in a lattice model

We shall consider a finite range model on a square latticeZ ³ and show the existence of bubble, tubular and lamellar phases by estimating the correlation functions at low temperature.