Modeling boyciana–fish–human interaction with partial differential algebraic equations

Abstract

Under the influence of human population distribution, the boyciana-fish ecological system is considered. First, the system can be described as a nonlinear partial differential algebraic equations system (PDAEs) with Neumann boundary conditions and ratio-dependent functional response. Second, we examine the system's persistence properties: the loacl stabilities of positive steady states, the absorbtion region and the global stability. And the proposed approach is illustrated by numerical simulation. Finally, by using the realistic data collected in the past fourteen years, the PDAEs parameter optimization model is built to predict the boyciana population.

On Explicit Stochastic Differential Algebraic Equations

“…From the application point of view, DAE is often used in control of physical/engineering systems such as in robotics [4,11,12], power engineering [20,9], aerodynamics [24], satellite applications [7] etc. Other than control, DAE also finds application in areas such as biochemistry [23,25], ecological sciences [10], astronomy and astrophysics [2], electromagnetism [8] etc. There is abundant literature on both theoretical and numerical aspects of DAEs.…”

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

“…analytical solution, 5,15 controllability and observability, 16 passivity criteria, see Reis and Jacob 17 and references therein). Jiang et al 1 resolved the local and global stability problem for SDPSs and the sufficient conditions of global stability were examined in the boyciana-fish ecological system. Based on the semi-group theory in Hilbert space, the exponential stability of the first-order SDPSs was concerned, and the sufficient conditions were derived in the work by Ge et al 18 Most of the existing studies have been done on the system Lyapunov asymptotic stability, which describes the asymptotic behavior of the state trajectory as time approaches infinity.…”

“…Singular distributed parameter systems (SDPSs), which governed by partial differential equations with singular matrix coefficient, are derived from the study of industrial distributed processes and physical phenomena under simplified assumptions such as the design of electronic circuits, 1 biological, economic models and one-dimensional (1D) drift-diffusion equation.. 2–4 The real world has provided a profound practical research background for SDPSs, such as involved in the fields of nanoelectronics, mechanical engineering, and electric networks. 5 The SDPS not only yields time-dependent systems of algebraic differential equations but also exhibits the spatial physical effects described by partial differential equations in space or time/space.…”

“…3,10,12,14,18 Second, many industrial and engineering processes can be governed by coupled partial differential equations with singular matrix coefficients, and the SDPSs have been of interest from a practical viewpoint. 1–5 Third, to the best of the authors’ knowledge, results on the control problem of FT stability and FT boundedness for SDPSs with parabolic type have not been investigated in the literature yet. In association with the above facts, this article aims to concern FT stability and FT boundedness for a class of parabolic SDPSs.…”

Variable structure control for a singular biological economic model with time delay and stage structure

“…Compared with the ordinary differential models, a singular system exhibits more complicated dynamics such as the impulse phenomenon [1]. Recently, many scholars proposed several kinds of biological dynamic systems [1,[3][4][5][6] by utilizing the theory of singular system, which studies the dynamic system with capture factors. According to the theory of T-S fuzzy descriptor system control, the control of a class of singular bioeconomic models with stage structure was studied in [5,7,8] by constructing a T-S fuzzy descriptor model.…”