Mingqing Xiao

Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control

In this paper, the synchronization problem for neural networks with stochastic perturbation is studied with intermittent control via adaptive aperiodicity. Under the framework of stochastic theory and Lyapunov stability method, we develop some techniques of intermittent control with adaptive aperiodicity to achieve the synchronization of a class of neural networks, modeled by stochastic systems. Some effective sufficient conditions are established for the realization of synchronization of the underlying network. Numerical simulations of two examples are provided to illustrate the theoretical results obtained in the paper.

New Criteria of Passivity Analysis for Fuzzy Time-Delay Systems With Parameter Uncertainties

This paper investigates the passivity problem for a class of uncertain stochastic fuzzy nonlinear systems with mixed delays and nonlinear noise disturbances by employing an improved free-weighting matrix approach. The fuzzy system is based on the Takagi-Sugeno model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, the parameter uncertainties, the stochastic disturbances, and nonlinearities are considered, where the parameter uncertainties enter into all the system matrices, the stochastic disturbances are given in the form of a Brownian motion. The mixed delays comprise both discrete and distributed time-varying delays. By taking the relationship among the time delays, their lower and upper bounds into account, some less conservative linear-matrix-inequality-based delay-dependent passivity criteria are obtained without ignoring any useful terms in the derivative of Lyapunov functional. Finally, numerical examples are given to demonstrate the effectiveness and merits of the proposed methods.

A new semi-smooth Newton multigrid method for control-constrained semi-linear elliptic PDE problems

In this paper a new multigrid algorithm is proposed to accelerate the convergence of the semi-smooth Newton method that is applied to the first order necessary optimality systems arising from a class of semi-linear control-constrained elliptic optimal control problems. Under admissible assumptions on the nonlinearity, the discretized Jacobian matrix is proved to have an uniformly bounded inverse with respect to mesh size. Different from current available approaches, a new numerical implementation that leads to a robust multigrid solver is employed to coarsen the grid operator. Numerical simulations are provided to illustrate the efficiency of the proposed method, which shows to be computationally more efficient than the full-approximation-storage multigrid in current literature. In particular, our proposed approach achieves a mesh-independent convergence and its performance is highly robust with respect to the regularization parameter.

Estimation of the diffusion rate and crossing probability for biased edge movement between two different types of habitat

One of the fundamental goals of ecology is to examine how dispersal affects the distribution and dynamics of insects across natural landscapes. These landscapes are frequently divided into patches of habitat embedded in a matrix of several non-habitat regions, and dispersal behavior could vary within each landscape element as well as the edges between elements. Reaction–diffusion models are a common way of modeling dispersal and species interactions in such landscapes, but to apply these models we also need methods of estimating the diffusion rate and any edge behavior parameters. In this paper, we present a method of estimating the diffusion rate using the mean occupancy time for a circular region. We also use mean occupancy time to estimate a parameter (the crossing probability) that governs one type of edge behavior often used in these models, a biased random walk. These new methods have some advantages over other methods of estimating these parameters, including reduced computational cost and ease of use in the field. They also provide a method of estimating the diffusion rate for a particular location in space, compared to existing methods that represent averages over large areas. We further examine the statistical properties of the new method through simulation, and discuss how mean occupancy time could be estimated in field experiments.

A leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problems

A new semi-smooth Newton multigrid algorithm is proposed for solving the discretized first order necessary optimality systems that characterizing the optimal solutions of a class of two dimensional semi-linear parabolic PDE optimal control problems with control constraints. A new computational scheme (leapfrog scheme) in time associated with the standard five-point stencil in space is established to achieve the second-order finite difference discretization. The convergence (or unconditional stability) of the proposed scheme is proved when assuming time-periodic solutions. Moreover, the derived well-structured discretized Jacobian matrices greatly facilitate the development of effective smoother in our multigrid algorithm. Numerical simulations are provided to illustrate the effectiveness of the proposed method, which validates the second-order accuracy in solution approximations and the optimal linear complexity of computing time.

Developmental variability and stability in continuous-time host–parasitoid models

Insect host-parasitoid systems are often modeled using delay-differential equations, with a fixed development time for the juvenile host and parasitoid stages. We explore here the effects of distributed development on the stability of these systems, for a random parasitism model incorporating an invulnerable host stage, and a negative binomial model that displays generation cycles. A shifted gamma distribution was used to model the distribution of development time for both host and parasitoid stages, using the range of parameter values suggested by a literature survey. For the random parasitism model, the addition of biologically plausible levels of developmental variability could potentially double the area of stable parameter space beyond that generated by the invulnerable host stage. Only variability in host development time was stabilizing in this model. For the negative binomial model, development variability reduced the likelihood of generation cycles, and variability in host and parasitoid was equally stabilizing. One source of stability in these models may be aggregation of risk, because hosts with varying development times have different vulnerabilities. High levels of variability in development time occur in many insects and so could be a common source of stability in host-parasitoid systems.

A Fast and Stable Preconditioned Iterative Method for Optimal Control Problem of Wave Equations

In this paper, we develop a new central finite difference scheme in terms of both time and space for solving the first-order necessary optimality systems that characterize the optimal control of wave equations. The obtained new scheme is proved to be unconditionally convergent with a second-order accuracy, without the requirement of the Courant--Friedrichs--Lewy condition on the corresponding grid ratio. An efficient preconditioned iterative method is further developed for solving the discretized sparse linear system based on the relationship between the resultant matrix structure and the coupled PDE optimality system. Numerical examples are presented to verify the theoretical analysis and to demonstrate the high efficiency of the proposed preconditioned iterative solver.

Variable prey development time suppresses predator–prey cycles and enhances stability

Although theoretical models have demonstrated that predator-prey population dynamics can depend critically on age (stage) structure and the duration and variability in development times of different life stages, experimental support for this theory is non-existent. We conducted an experiment with a host-parasitoid system to test the prediction that increased variability in the development time of the vulnerable host stage can promote interaction stability. Host-parasitoid microcosms were subjected to two treatments: Normal and High variance in the duration of the vulnerable host stage. In control and Normal-variance microcosms, hosts and parasitoids exhibited distinct population cycles. In contrast, insect abundances were 18-24% less variable in High- than Normal-variance microcosms. More significantly, periodicity in host-parasitoid population dynamics disappeared in the High-variance microcosms. Simulation models confirmed that stability in High-variance microcosms was sufficient to prevent extinction. We conclude that developmental variability is critical to predator-prey population dynamics and could be exploited in pest-management programs.

Approximately nearly controllability of discrete-time bilinear control systems with control input characteristic

Abstract In this paper we study a class of discrete-time bilinear control systems that can be used to model the production storage management problems. A weaker but more applicable concept of controllability, approximately nearly controllability, is proposed under the framework of hypercyclicity from the theory of dynamical systems. The complete characteristic of the system structure for being approximately nearly controllable is provided. Necessary and sufficient conditions for the system to be approximately nearly controllable are presented. Moreover, the required number of different input values for the system to achieve the approximately nearly controllability during the evolutionary process is obtained.

Identification of diffusion coefficient in nonhomogeneous landscapes

Diffusion models have been found in various applications in the study of spatial population dynamics for modeling the species dispersal process in natural environments. Diffusion coefficient is a critical parameter in diffusion equations. In this paper, a new method for estimating the diffusion coefficient of insects is presented in terms of occupancy time and the method can produce any desired accuracy. The study of modeling biological organism movement behaviors in a nonhomogeneous landscape is critical in investigating the interplay between environmental heterogeneity and organism movements. By constructing a set of eigenvalues, we can characterize the insect biased movement when insect crosses the intersection of two different type of landscape elements. Some numerical examples are provided to illustrate the theoretical outcomes obtained in the paper.