Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems

The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.

PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION

A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion systemwhere ai(t),bi(t) and Di(t)(i = 1, 2) axe positive continuous T-periodic functions, gi(t,xi) (i = 1,2) and h(t,y) are continuous and T-periodic with respect to t and h(t,y) > 0 for y>0,t, y∈R,pi(x)(i=1,2) are continuous and monotonously increasing functions, and Pi(xi)>0 for xi>0.

Global Asymptotic Stability and Hopf Bifurcation in a Homogeneous Diffusive Predator-Prey System with Holling Type II Functional Response

In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.

STABILITY ANALYSIS OF LINEAR AND NONLINEAR PERIODIC CONVECTION IN THERMOHALINE DOUBLE－DIFFUSIVE SYSTEMS

A shortout analytic method of stability in Strong nonlinear autonomous system is introduced into stability analysis of the themohaline double-diffusive system.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimeal motion the existence range of monotomic branch and oscillatory branch are outilined.The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value μc in this case of 0<rs-rsc<<1The stability conclusions under different direction of vortex are drawn out .

Bifurcationing Analysis of Predator-Prey Diffusive System Based on Bazykin Functional Response

A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.

INVASION TRAVELING WAVES FOR A DISCRETE DIFFUSIVE RATIO-DEPENDENT PREDATOR-PREY MODEL

This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c* such that when c > c* , the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c* is also established by a limiting argument and a delicate analysis of the boundary conditions.Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c* is also proved.

Analysis of diffusion-adsorption equivalency of landfill liner systems for organic contaminants

The equivalence between multilayered barriers regarding diffusion and adsorption was studied. The bottom boundary of the liner system is defined by assuming concentration continuous and flux continuous conditions of the contaminant between the bottom liner layer and the underlying soil. Five different liner systems were compared in terms of solute breakthrough time. The results of the analysis showed that breakthrough time of the hydrophobic organic compounds for a 2-meter-thick compacted clay liner （CCL） could be 3-4 orders of magnitude is greater than the breakthrough time for a geosynthetic clay liner （GCL） composite liner. The GM/GCL and GM/CCL composite liner systems provide a better diffusion barrier for the hydrophilic organic compounds than that for the hydrophobic compounds due to their different Henry＇s coefficient. The calculated breakthrough times of the organic contaminants for the Chinese standard liner systems were found to be generally greater than those for the GCL alternatives, for the specific conditions examined. If the distribution coefficient increases to 2.8 for the hydrophobic compounds or 1.0 for the hydrophilic compounds, the thickness of the attenuation layer needed to achieve the same breakthrough time as the standard liner systems can be reduced by a factor of about 1.9-2.4. As far as diffusive and adsorption contaminant transport are concerned, GM or GCL is less effective than CCL.

Self-Similar Solutions for a Class of Reaction-Diffusion Systems

The self similar solutions for a class of reaction diffusion systems are analyzed. The existence and qualitative properties are discussed.

A Class of Nonlinear Nonlocal Singularly Perturbed Reaction Diffusion Systems

The singularly perturbed initial boundary value problems for the reaction diffusion system are raised. Firstly, under suitable conditions, using a iteration technique, the differential inequalities theorem is constructed and introducing two auxiliary functions the existence and uniqueness theorem of solution for the basic reaction diffusion system is proved. Using the singularly perturbed method the formal asymptotic expressions of the solution are constructed with power series theory. By using the comparison theorem the existence and its asymptotic behavior of solution for the original problem are studied. Finally, using method of estimate inequalities, the structure of solutions for the problem is discussed thoroughly in three cases and asymptotic solution of the original problem is given. The asymptotic behavior of solution in the three cases is proved.

EXISTENCE OF SOLUTIONS FOR GRADIENT SYSTEMS WITH APPLICATION TO DIFFUSION PROBLEMS INVOLVING NONCONVEX ENERGIES

In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations involving nonconvex energies.

The Nonlinear Predator-Prey Singularly Perturbed Robin Initial Boundary Value Problems for Reaction Diffusion System

The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

Global Bounded Solutions for Reaction-diffusion Systems with a Full Matrix of Diffusion Coefficients and a Balance Law

This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.

Global attractors associated with general partly dissipative reaction-diffusion systems in unbounded domains

The asymptotic behaviour of solutions for general partly dissipative reaction-diffusion systems in Rn is studied. The asymptotic compactness of the solutions and then the existence of the global attractor are proved in L2(Rn )× L2(Rn ) .

Critical Fujita Exponents for Localized Reaction Diffusion Systems

In this paper, we prove the existence of cirtical Fujita exponents for a class of localized reaction diffusion systems.

Dynamics Behaviors of a Reaction-Diffusion Predator-Prey System with Beddington-DeAngelis Functional Response and Delay

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response and a discrete time delay. By introducing a partial quasi-monotonicity condition and constructing a pair of upper-lower solutions, we establish the existence of traveling wave solutions. Moreover, a numerical simulation is carried out to illustrate the theoretical results.

Research on Policy Diffusion Path and Reproduction of River Chief System

The River Chief System (RCS) has evolved from local innovative practices to a national water governance strategy to address the current challenges in China’s water environmental management. In contrast to existing research that focuses on the strengths, weaknesses, and improvements of RCS, this study uses literature study to reveal the dynamic evolution of RCS through three phases, with RCS spreading from developed coastal areas to central and western inland regions. RCS’s diffusion path involves vertical diffusion between central and local levels and horizontal diffusion among local governments. Moreover, RCS has also achieved conceptual spillover, gradually expanding into other governance domains, such as the Lake Chief System, the Field Chief System, the Forestry Chief System, and the integration of multiple chief roles. However, it is essential to scrutinize the phenomenon of applying similar governance mechanisms to different areas, as it may result in challenges such as overburdening local governments, insufficient public participation, oversimplification of differences in natural resource endowments, and limited applicability. This study also provides suggestions on how to address these challenges. The study contributes theoretical insights and policy implications, providing a foundation for practical policy innovation.

Periodic Solution for Stochastic Predator-Prey Systems with Nonlinear Harvesting and Impulses

In this paper, astochastic predator-prey systems with nonlinear harvesting and impulsive effect are investigated. Firstly, we show the existence and uniqueness of the global positive solution of the system. Secondly, by constructing appropriate Lyapunov function and using comparison theorem with an impulsive differential equation, we study that a positive periodic solution exists. Thirdly, we prove that system is globally attractive. Finally, numerical simulations are presented to show the feasibility of the obtained results.

MapReduce based computation of the diffusion method in recommender systems

The performance of existing diffusion-based algorithms in recommender systems is still limited by the processing ability of a single computer. In order to conduct the diffusion computation on large data sets,a parallel implementation of the classic diffusion method on the MapReduce framework is proposed. At first,the diffusion computation is transformed from a summation format to a cascade matrix multiplication format,and then,a parallel matrix multiplication algorithm based on dynamic vector is proposed to reduce the CPU and I / O cost on the MapReduce framework,which can also be applied to other parallel matrix multiplication scenarios. Then,block partitioning is used to further improve the performance,while the order of matrix multiplication is also taken into consideration.Experiments on different kinds of data sets have verified the efficiency of the proposed method.