Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure

Abstract

Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discrete predator-prey system where the population diffusion is based on the Moore neighborhood structure instead of the von Neumann neighborhood structure widely applied previously. Under pattern formation conditions which are determined by Turing instability analysis, numerical simulations are performed to reveal the spatiotemporal complexity of the system. A pure Turing instability can induce the self-organization of many basic types of patterns as described in the literature, as well as new spiral-spot and labyrinth patterns which show the temporally oscillating and chaotic property. Neimark-Sacker-Turing and flip-Turing instability can lead to the formation of circle, spiral and much more complex patterns, which are self-organized via spatial symmetry breaking on the states that are homogeneous in space and non-periodic in time. Especially, the emergence of spiral pattern suggests that spatial order can generate from temporal disorder, implying that even when the predator-prey dynamics in one site is chaotic, the spatially global dynamics may still be predictable. The results obtained in this research suggest that when the way of population diffusion changes, the pattern formation in the predator-prey systems demonstrates great differences. This may provide realistic significance to explain more general predator-prey coexistence.

Suppression gene drive in continuous space can result in unstable persistence of both drive and wild‐type alleles

“…Perhaps most obviously, the chasing of wild‐type alleles by a suppression gene drive invokes a conceptual analogy to classical predator–prey systems, where spatial structure was found to generally promote the coexistence of areas dominated by predators, prey and empty space (Chang et al, 2019; Donalson & Nisbet, 1999; Gilpin & Feldman, 2017; Huang et al, 2019, 2019.). However, it is not yet clear whether a one‐to‐one mapping between these systems is indeed possible.…”

Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions

“…As a result, Figure 5 shows the pattern, including the dynamic properties of both, and contains new collective dynamical behavior. Figure 5 shows that against the background of synchronous dynamics (cluster 4), two clusters arise around subpopulations with the coordinates (18,30) and (30,20). These clusters merge and form the group of intersecting clusters after a series of transients (Figure 5a,b).…”

“…According to ecologists, a habitat is seldom described by a torus but is widely used by mathematicians. For instance, this scenario is used to simulate spatio-temporal dynamics for continuous space (reaction-diffusion equations) [13,17,19] and for discrete space (ensembles of nonlinear oscillators) [2,12,14,18,31,32]. This range description is especially used in cellular automata and individual-based models [64,65].…”

“…If the local population has an age structure (overlapping generations), then the local dynamics are described by a two-or more dimensional map [6][7][8][9][10]. A local structure, involving interspecific interactions, often arises for the study of metacommunitie, that is, ecological communities of predator-prey or host-parasite systems coupled by migration [11][12][13][14][15][16][17][18][19].…”

Dynamics Analysis of Modified Leslie-Gower Model with Simplified Holling Type IV Functional Response

“…Penelitian selanjutnya, Huang [6] melakukan Nur Suci Ramadhani, Syamsuddin Toaha, Kasbawati analisis bifurkasi pada model Leslie-Gower dengan pertumbuhan logistik pada mangsa dan menggunakan fungsi respon Holling tipe IV yang disederhanakan. Huang, T., dkk [7] melakukan analisis pembentukan pola terhadap model Lotka-Volterra dengan fungsi respon Holling tipe IV yang disederhanakan. Khajanchi [8] melakukan analisis pada sistem mangsa pemangsa tahapan struktur dengan fungsi respon Holling tipe IV yang disederhanakan.…”