Study of cross-diffusion induced Turing patterns in a ratio-dependent prey-predator model via amplitude equations

Bloom Formation and Turing Patterns in an Infochemical Mediated Multitrophic Plankton Model

“…It will be interesting to study the existence and stability of the spot solutions using geometric techniques as employed in, e.g., [Harley et al, 2014[Harley et al, , 2015. Studying whether such solutions persist in two-dimension and become actual coldspots or hotspots (which are localised in both directions) or 'cold-stripes' and 'hot-stripes' (which are localised in one direction but constant in the perpendicular one), see, e.g., [Banerjee & Volpert, 2017;Banerjee et al, 2018;Rodrigues et al, 2011], is also intriguing and addressed for future work. Additionally, our analysis in this paper is concentrated on standing patterns.…”

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

“…In Holling type IV functional response, predators cannot survive above some upper threshold of prey density. To incorporate these effects into predator-prey interactions, many predator-prey models have been proposed (e.g., [12][13][14][15][16][17], just to mention a few). Recently, in [18], the authors have considered a model describing the predator-prey interaction, introducing the group defense of prey through the Holling type IV functional response and the reduction of prey growth rate, represented as a fear factor, in the presence of group defense through Monod-Haldane type functional response.…”

“…In particular, diffusion-driven instability, commonly known as Turing instability, leads to the occurrence of the so-called Turing patterns. The study of these patterns in spatial population models has recently seen an increasing activity and interest ( [14,15,23,[27][28][29][30]). Motivated by all these considerations, we include both self-diffusion and cross-diffusion into (1) and study the following system…”

Characterizing the Effects of Self- and Cross-Diffusion on Stationary Patterns of a Predator–Prey System

“…In this connection, we must point out, Shigesada, Kawasaki and Teramoto first proposed a strongly coupled reaction-diffusion model with Lotka-Volterra type reaction terms to investigate the more complex ecological phenomenon such as spatial segregation of interacting population species in onedimensional space [Shigesada et al, 1979]. The readers can also see [Banerjee et al, 2018;Cantrell & Cosner, 2001;Lou & Ni, 1996;Madzvamuse et al, 2015;Mukherjeeet al, 2018;Ni & Tang, 2005;Sun et al, 2012;Tulumello et al, 2014] for this aspect.…”