Journal of Mathematical Analysis and Applications, Journal Year: 2024, Volume and Issue: 541(1), P. 128683 - 128683
Published: July 14, 2024
Language: Английский
Journal of Mathematical Chemistry, Journal Year: 2025, Volume and Issue: unknown
Published: Jan. 28, 2025
Language: Английский
Citations
5
Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: 112(13), P. 11615 - 11636
Published: May 15, 2024
Language: Английский
Citations
7
Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 186, P. 115287 - 115287
Published: July 23, 2024
This work aims at elucidating the conditions under which stationary and oscillatory periodic patterns may emerge in a class of one-dimensional three-compartments reaction–diffusion models where one interacting species does not undergo any spatial dispersal. To this purpose, linear stability analysis is firstly employed to deduce system undergoes Turing or wave instability as well extract information on main features that characterize corresponding patterned solutions onset. Then, multiple-scale weakly nonlinear carried out describe time evolution pattern amplitude close bifurcation thresholds above-mentioned instabilities. Finally, provide quantitative estimation most relevant features, an illustrative example context dryland ecology addressed. It deals with generalization Klausmeier vegetation model for flat arid environments describes interaction among biomass, soil water toxic compounds. Numerical simulations are also used corroborate theoretical findings gain some useful insights into ecological response ecosystems variable environmental conditions.
Language: Английский
Citations
5
Mathematical Methods in the Applied Sciences, Journal Year: 2024, Volume and Issue: unknown
Published: Sept. 11, 2024
In semiarid areas, the positive feedback effect of vegetation and soil moisture plays an indispensable role in water absorption process plant roots. addition, can absorb through nonlocal interaction Therefore, this article, we consider how interactions between cross‐diffusion delay affect growth. Through mathematical analysis, conditions for occurrence Turing pattern water–vegetation model are obtained. Meanwhile, using multi‐scale analysis method, amplitude equation near bifurcation boundary is By analyzing stability equation, appearance patterns such as stripes, hexagons, mixtures stripes hexagons determined. Some numerical simulations given to illustrate analytical results, especially evolution processes depicted under different parameters.
Language: Английский
Citations
4
Studies in Applied Mathematics, Journal Year: 2025, Volume and Issue: 154(2)
Published: Feb. 1, 2025
ABSTRACT In this paper, based on the importance of consumer memory spatial resource distribution, we propose a novel consumer‐resource model that incorporates nonlocal discrete memory. By conducting thorough bifurcation and stability analysis, determine conditions for occurrence Hopf Turing bifurcations reveal unique dynamic phenomenon termed Turing–Hopf bifurcation, which is uncommon in models without We also show as delay increases, both spatially nonhomogeneous periodic steady‐state solutions may vanish, unstable positive homogeneous steady state regain stability. Furthermore, leveraging theory normal forms, derive new effective algorithm to direction where diffusion component an integral term with delay. addition, perform numerical simulations validate our theoretical findings, particularly assess delay‐induced mode‐1 bifurcation. Our method used purpose, results have been confirmed by rigorous analysis.
Language: Английский
Citations
0
The Science of The Total Environment, Journal Year: 2024, Volume and Issue: 951, P. 175517 - 175517
Published: Aug. 13, 2024
Language: Английский
Citations
1
Complex Variables and Elliptic Equations, Journal Year: 2024, Volume and Issue: unknown, P. 1 - 33
Published: Oct. 21, 2024
A diffusive phytoplankton–zooplankton–fish model with toxin and Crowley–Martin functional response is considered. By the global bifurcation theorem fixed point index theory, existence multiplicity of coexistence states are discussed. Secondly, we investigate from a double eigenvalue by virtue Lyapunov–Schmidt procedure implicit function theorem. Then, effect large k, which measures magnitude interference among zooplankton, studied means combination perturbation theory topological degree theory. The results indicate that if k enough, this system has only unique asymptotically stable state provided properly small maximal growth rates phytoplankton fish suitably large. Furthermore, extinction permanence time-dependent determined comparison principle. Finally, make some numerical simulations to validate complement theoretical analysis exhibit critical role toxin, spatial diffusion zooplankton in dynamics. findings suggest spatiotemporal dynamics systems richer more complex, have significant effects on species.
Language: Английский
Citations
1
Journal of Mathematical Analysis and Applications, Journal Year: 2024, Volume and Issue: 538(1), P. 128334 - 128334
Published: March 21, 2024
Language: Английский
Citations
0
Results in Physics, Journal Year: 2024, Volume and Issue: 61, P. 107792 - 107792
Published: May 23, 2024
Time-delay effect and bifurcation phenomenon are important topics in the study of reaction–diffusion equations. In this paper, we consider a three-species predator–prey system with diffusion incubation delay for predator. The stability Hopf mainly discussed. We conclude that there exists critical value delay, such internal equilibrium is stable or unstable as crosses value. Especially, emerges at For solution, conclusions stability, period direction also presented. Additionally, numerical simulations proceeded to support main results. biology, existence solution means when predator reaches certain extent, prey will coexist within time. It turns out related computations analyses much more complicated than two-species time-delay systems.
Language: Английский
Citations
0
Acta Applicandae Mathematicae, Journal Year: 2024, Volume and Issue: 192(1)
Published: July 1, 2024
Language: Английский
Citations
0