Analysis of patterns in an additional food-provided predator-prey reaction diffusion model using amplitude equations

Küçük Resim Yok

Tarih

2023

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Indian Acad Sciences

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

A two-species predator-prey reaction diffusion model where additional food was provided to the predator has been considered in the presence of both self- and cross-diffusion terms in a two-dimensional space. Importance of self- and cross-diffusion terms are discussed ecologically. Linear stability analysis has been done to determine the Turing instability region of the parameter space. Impacts of the cross-diffusion term on the stability behaviour are discussed. Using weak nonlinear analysis, the amplitude equations has been formulated to predict the stability of hexagonal, stripes and their mixture patterns near the Turing thresholds analytically. Finite difference method has been used for numerical simulations of the model under no-flux boundary conditions. Numerical simulation results are in good agreement with the theoretical predictions of patterns near the Turing threshold using amplitude equations. Additional food can play a significant role in pattern forming instabilities because near the Turing thresholds small fluctuation of additional food parameter can produce a wide variety of Turing patterns.

Açıklama

Anahtar Kelimeler

Additional food, cross diffusion, bifurcation, amplitude equation, pattern formation, chaos, 05.45.Xt, 05.45.Jn, 02.70.Cn, 02.60.Cb, 52.35.Mw

Kaynak

Pramana-Journal of Physics

WoS Q Değeri

Q2

Scopus Q Değeri

Q2

Cilt

97

Sayı

4

Künye