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1.
Huicong Li;Tian Xiang; 《Studies in Applied Mathematics》2024,153(1):e12683
We study global existence, boundedness, and convergence of nonnegative classical solutions to a Neumann initial-boundary value problem for the following possibly cross-diffusive SIS (susceptible–infected–susceptible) epidemic model with power-like infection mechanism generalizing the standard mass action incidence: 相似文献
2.
Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function. 相似文献
3.
Yuanqu Lin 《中国科学A辑(英文版)》1998,41(6):613-621
The existence of a bounded global attractor for a cross-diffusion model of forest with homogeneous Dirichlet boundary condition
is proved under some condition on the parameters
Project supported by the National Natural Science Foundation of China (Grant No. 19671005). 相似文献
4.
本文研究带齐次Dirichlet边界条件的强耦合椭圆系统,首先证明了当食饵和捕食者的扩散率足够大,或者出生率足够小时,系统不存在共存现象,并给出半平凡解存在的充分条件．然后利用Schauder不动点定理,得到强耦合的椭圆问题至少有一个正解存在的充分条件．该条件说明只要捕食者的内部竞争强,物种的交叉扩散相对弱,或者捕获率足够小,物种的交叉扩散相对弱,强耦合系统就至少有一个正解存在． 相似文献
5.
三种群食物链交错扩散模型的整体 总被引：1，自引：0，他引：1
本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性,该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件． 相似文献
6.
We consider a strongly coupled nonlinear parabolic system which arises in population dynamics in -dimensional domains (). Global existence of classical solutions under certain restrictions on the coefficients is established.
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8.
Yong-Jung Kim ;Changwook Yoon 《Discrete and continuous dynamical systems》2023,28(12):6289-6305
Keller-Segel equations are widely employed to explain chemotaxis-induced bacterial traveling band phenomena. In this system, the dispersal of bacteria is modeled by independently given diffusion and advection terms, and the growth of cell population is neglected. In the paper, we develop a chemotaxis model which consists of cross-diffusion and population growth. In particular, we consider the case that the diffusion and advection terms form an exact cross-diffusion. The developed mathematical models are based on the conversion dynamics between active and inactive cells with different dispersal rates. The process consists of three steps and the performance of each step is complemented by comparing numerical simulations and experimental data. 相似文献
9.
In this paper, we present the amplitude equations for the excited modes in a cross-diffusive predator--prey model with zero-flux boundary conditions. From these equations, the stability of patterns towards uniform and inhomogenous perturbations is determined. Furthermore, we present novel numerical evidence of six typical turing patterns, and find that the model dynamics exhibits complex pattern replications: for μ1<μ≤μ2, the steady state is the only stable solution of the model; for μ2<μ≤μ4, by increasing the control parameter μ, the sequence Hπ-hexagons → H0-hexagon-stripe mixtures rightarrow stripes → Hπ-hexagon-stripe mixtures → H0-hexagons is observed; for μ>μ4, the stripe pattern emerges. This may enrich the pattern formation in the cross-diffusive predator--prey model. 相似文献
10.
Yanhua Zhu You Li Xiangyi M Ying Sun Ziwei Wang Jinliang Wang 《Journal of Applied Analysis & Computation》2025,15(2)
This paper presents a study on spatiotemporal dynamics and Turing patterns in a space-time discrete depletion type Gierer-Meinhardt model with self-diffusion and cross-diffusion based on coupled map lattices (CMLs) model. Initially, the existence and stability conditions for fixed points are determined through linear stability analysis. Secondly, the conditions for the occurrence of flip bifurcation, Neimark–Sacker bifurcation, and Turing bifurcation are derived by means of the center manifold reduction theorem and bifurcation theory. The results indicate that there exist two nonlinear mechanisms, namely flip-Turing instability and Neimark–Sacker-Turing instability. Additionally, some numerical simulations are performed to illustrate the theoretical findings. Interestingly, a rich variety of dynamical behaviors, including period-doubling cascades, invariant circles, periodic windows, chaotic regions, and striking pattern formations (plaques, mosaics, curls, spirals, and other intermediate patterns), are observed. Finally, the evolution of pattern size and type is also simulated as the cross-diffusion coefficient varies. It reveals that cross-diffusion has a certain influence on the growth of patterns. 相似文献