The Stochastic Coupling of SLE on the Strip Domain

The main work of this paper is to discuss the stochastic coupling of stirp SLEk (k ∈ (0,4]) on the stirp region Sπ. By constructing a bounded continuous local martingale, we prove that when a certain ordinary differential equation is satisfied, there is a coupling of two strip SLEk traces in Sπ;one is from a to b;the other is from b to a, such that the two curves visit the same set of points.

Synchronization of stochastically hybrid coupled neural networks with coupling discrete and distributed time-varying delays

A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed, which is composed of constant coupling, coupling discrete time-varying delay and coupling distributed timevarying delay. All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion, which reflects a more realistic dynamical behaviour of coupled systems in practice. Based on a simple adaptive feedback controller and stochastic stability theory, several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays. Finally, numerical simulations illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.

A Comparison Theorem for Solution of the Fully Coupled Backward Stochastic Differential Equations

The comparison theorems of solutions for BSDEs in fully coupled forward-backward stochastic differential equations (FBSDEs) are studied in this paper, here in the fully coupled FBSDEs the forward SDEs are the same structure.

Stochastic fluctuations of permittivity coupling regulate seizure dynamics in partial epilepsy

Partial epilepsy is characterized by recurrent seizures that arise from a localized pathological brain region. During the onset of partial epilepsy, the seizure evolution commonly exhibits typical timescale separation phenomenon. This timescale separation behavior can be mimicked by a paradigmatic model termed as Epileptor, which consists of coupled fast-slow neural populations via a permittivity variable. By incorporating permittivity noise into the Epileptor model, we show here that stochastic fluctuations of permittivity coupling participate in the modulation of seizure dynamics in partial epilepsy. In particular, introducing a certain level of permittivity noise can make the model produce more comparable seizure-like events that capture the temporal variability in realistic partial seizures. Furthermore, we observe that with the help of permittivity noise our stochastic Epileptor model can trigger the seizure dynamics even when it operates in the theoretical nonepileptogenic regime. These findings establish a deep mechanistic understanding on how stochastic fluctuations of permittivity coupling shape the seizure dynamics in partial epilepsy,and provide insightful biological implications.

Euler-type schemes for weakly coupled forward-backward stochastic differential equations and optimal convergence analysis

We introduce a new Euler-type scheme and its iterative algorithm for solving weakly coupled forward-backward stochastic differential equations （FBSDEs）. Although the schemes share some common features with the ones proposed by C. Bender and J. Zhang [Ann. Appl. Probab., 2008, 18： 143-177], less computational work is needed for our method. For both our schemes and the ones proposed by Bender and Zhang, we rigorously obtain first-order error estimates, which improve the half-order error estimates of Bender and Zhang. Moreover, numerical tests are given to demonstrate the first-order accuracy of the schemes.

A Compact Scheme for Coupled Stochastic Nonlinear Schrodinger Equations

In this paper,we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrodinger equations.We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law,discrete charge conservation law and discrete energy evolution law almost surely.Numerical experiments confirm well the theoretical analysis results.Furthermore,we present a detailed numerical investigation of the optical phenomena based on the compact scheme.By numerical experiments for various amplitudes of noise,we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time.In particular,if the noise is relatively strong,the soliton will be totally destroyed.Meanwhile,we observe that the phase shift is sensibly modified by the noise.Moreover,the numerical results present inelastic interaction which is different from the deterministic case.

Synchronization-Based Topology Identification of Uncertain Stochastic Delay Complex Networks

In this paper, topology identification of general weighted complex network with time-varying delay and stochastic perturbation,which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established, which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances, as well as identify the topological structure of the uncertain general drive complex network. Finally, numerical simulations are presented to verify the correctness and effectiveness of the proposed scheme.

A critical transition rule for broadening exponent of fluctuation and its effect on dissipation in chemical reaction-heat conduction coupling systems

A stochastic model of chemical reaction-heat conduction-diffusion for a one-dimensional gaseous system under Dirichlet or zero-fluxes boundary conditions is proposed in this paper. Based on this model,we extend the theory of the broadening exponent of critical fluctuations to cover the chemical reaction-heat conduction coupling systems as an asymptotic property of the corresponding Markovian master equation (ME),and establish a valid stochastic thermodynamics for such systems. As an illustration,the non-isothermal and inhomogeneous Schl-gl model is explicitly studied. Through an order analysis of the contributions from both the drift and diffusion to the evolution of the probability distribution in the corresponding Fokker-Planck equation(FPE) in the approach to bifurcation,we have identified the critical transition rule for the broadening exponent of the fluctuations due to the coupling between chemical reaction and heat conduction. It turns out that the dissipation induced by the critical fluctuations reaches a deterministic level,leading to a thermodynamic effect on the nonequilibrium physico-chemical processes.

Stability of Coupled Impulsive Markovian Jump Reaction-Diffusion Systems on Networks

This paper is devoted to the investigation of stability for a class of coupled impulsive Markovian jump reaction-diffusion systems on networks(CIMJRDSNs). By using graph theory, a systematic method is provided to construct global Lyapunov functions for the CIMJRDSNs. Based on Lyapunov functions and stochastic analysis method, some novel stability principles associated with the topology property of the networks are established.

Near-Relaxed Control Problem of Fully Coupled Forward-Backward Doubly System

In this paper,we are concerned with an optimal control problem where the system is driven by a fully coupled forward-backward doubly stochastic differential equation.We study the relaxed model for which an optimal solution exists.This is an extension of initial control problem,where admissible controls are measure valued processes.We establish necessary as well as sufficient optimality conditions to the relaxed one.