Pattern dynamics and Turing instability induced by self-super-cross-diffusive predator-prey model via amplitude equations

被引:5
作者
Iqbal, Naveed [1 ]
Wu, Ranchao [2 ]
Karaca, Yeliz [3 ]
Shah, Rasool [4 ]
Weera, Wajaree [5 ]
机构
[1] Univ Hail, Coll Sci, Dept Math, Hail, Saudi Arabia
[2] Anhui Univ, Sch Math Sci, Anhui 230601, Peoples R China
[3] Univ Massachusetts, Med Sch, Worcester, MA 01655 USA
[4] Abdul Wali Khan Univ, Dept Math, Mardan 23200, Pakistan
[5] Khon Kaen Univ, Fac Sci, Dept Math, Khon Kaen 40002, Thailand
来源
AIMS MATHEMATICS | 2023年 / 8卷 / 02期
关键词
Turing instability; amplitude equations; self-super-cross-diffusion; pattern formation; stability analysis; weakly nonlinear analysis (WNA); POSITIVE STEADY-STATES; SYSTEM;
D O I
10.3934/math.2023153
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Incorporating self-diffusion and super-cross diffusion factors into the modeling approach enhances efficiency and realism by having a substantial impact on the scenario of pattern formation. Accordingly, this work analyzes self and super-cross diffusion for a predator-prey model. First, the stability of equilibrium points is explored. Utilizing stability analysis of local equilibrium points, we stabilize the properties that guarantee the emergence of the Turing instability. Weakly nonlinear analysis is used to get the amplitude equations at the Turing bifurcation point (WNA). The stability analysis of the amplitude equations establishes the conditions for the formation of small spots, hexagons, huge spots, squares, labyrinthine, and stripe patterns. Analytical findings have been validated using numerical simulations. Extensive data that may be used analytically and numerically to assess the effect of self-super-cross diffusion on a variety of predator-prey systems.
引用
收藏
页码:2940 / 2960
页数:21
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