Stationary Distribution and Extinction of a Stochastic Microbial Flocculation Model with Regime Switching

In this paper, a stochastic microbial flocculation model with regime switching is developed and analyzed. By proposing a suitable stochastic Lyapunov function, the existence and ergodicity of a stationary distribution for the system are proved. Then, the extinction of microorganisms is discussed under appropriate conditions and sufficient conditions for extinction are obtained. Finally, the results of the theoretical analysis are illustrated by numerical simulation.

Dynamics of a stochastic SIRS epidemic model with standard incidence under regime switching

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.

Analysis on stochastic predator-prey model with distributed delay

In the present work, we consider a stochastic predator-prey model with disease in prey and distributed delay. Firstly, we establish sufficient conditions for the extinction of the disease and also permanence of healthy prey and predator. Besides, we obtain the condition for the existence of an ergodic stationary distribution through the stochastic Lyapunov function. Finally, we provide some numerical simulations to validate our theoretical findings.

Stochastic SIRC epidemic model with time-delay for COVID-19

Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number ${\mathcal{R}}_{0}^{s}$ R 0 s for the stochastic model which is smaller than ${\mathcal{R}}_{0}$ R 0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.

Dynamical Behavior of a Stochastic SIRC Model for Influenza A

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

An Event-Triggered Fault Detection Approach in Cyber-Physical Systems with Sensor Nonlinearities and Deception Attacks

In this paper, a general event-triggered framework is constructed to investigate the problem of remote fault detection for stochastic cyber-physical systems subject to the additive disturbances, sensor nonlinearities and deception attacks. Both fault-detection residual generation and evaluation module are fully described. Two energy norm indices are presented so that the fault-detection residual has the best sensitivity to faults and the best robustness to unwanted factors including additive disturbances and false information injected by attacker. Moreover, the filter gain and residual weighting matrix are formulated in terms of stochastic Lyapunov function, which can be conveniently solved via standard numerical software. Finally, an application example is presented to verify the performance of fault detection by comparative simulations. The prolonged battery life is experimentally evaluated and analyzed via a wireless node platform.

A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold Rs 0 which is different from that given in [22] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When Rs0 > 0, the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [22] is improved and extended.

STOCHASTIC GRADIENT LEARNING AND INSTABILITY: AN EXAMPLE

In this paper, we investigate real-time behavior of constant-gain stochastic gradient (SG) learning, using the Phelps model of monetary policy as a testing ground. We find that whereas the self-confirming equilibrium is stable under the mean dynamics in a very large region, real-time learning diverges for all but the very smallest gain values. We employ a stochastic Lyapunov function approach to demonstrate that the SG mean dynamics is easily destabilized by the noise associated with real-time learning, because its Jacobian contains stable but very small eigenvalues. We also express caution on usage of perpetual learning algorithms with such small eigenvalues, as the real-time dynamics might diverge from the equilibrium that is stable under the mean dynamics.

Stabilization of Semi-Markovian Jump Systems with Uncertain Probability Intensities and Its Extension to Quantized Control

This paper concentrates on the issue of stability analysis and control synthesis for semi-Markovian jump systems (S-MJSs) with uncertain probability intensities. Here, to construct a more applicable transition model for S-MJSs, the probability intensities are taken to be uncertain, and this property is totally reflected in the stabilization condition via a relaxation process established on the basis of time-varying transition rates. Moreover, an extension of the proposed approach is made to tackle the quantized control problem of S-MJSs, where the infinitesimal operator of a stochastic Lyapunov function is clearly discussed with consideration of input quantization errors.