Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion

Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.

Sistem Predasi dalam Dinamika Populasi

Paper ini berkaitan dengan system predasi dalam Dinamika Populasi. Paper ini disusun dalam memperluas ilmu tentang dasar dan manfaat pembelajaran dinamika populasiberdasarkan pengamatan dari berbagai sumber informasi yang dijadikan sebagai referensi. Semoga paper ini dapat memberikan wawasan yang lebih luas dan menjadi sumbangan pemikiran kepada pembaca khususnya para mahasiswa. Predasi merupakan hubunganantara predator (pemangsa) dan prey (mangsa). Pada predasi sendiri terdapat dua model yang mendeskripsikan interaksi dua spesies terdiri dari predator dan prey merupakanmodel predator-prey. Model predator- prey sederhana ini diperkenalkan Lotka- Voltera yang kemudian di modifikasi oleh Leslie Gower. Hubungan antar spesies dapat dikelompokkan menjadi netralisme, mutualisme, parasitisme, predatorisme, kooperasi, kompetisi, komensalisme, dan antagonis.

Dynamics and bifurcations of a ratio-dependent predator-prey model

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Complexity of a Discrete-Time Predator-Prey Model Involving Prey Refuge Proportional to Predator

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.