Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices
Host–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasi...
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2024-12-01
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| author | Shuo Liang Wenlong Wang Chunrui Zhang |
| author_facet | Shuo Liang Wenlong Wang Chunrui Zhang |
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| description | Host–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasitoid, while the parasitoid depends on the host to complete its life cycle. This paper investigates the effect of parasitoid aggregation attacks on a host in a host–parasitoid model with self-diffusion on two-dimensional coupled map lattices. We assume that in the simulation of biological populations on a plane, the interactions between individuals follow periodic boundary conditions. The primary objective is to analyze the complex dynamics of the host–parasitoid interaction model induced by an aggregation effect and diffusion in a discrete setting. Using the aggregation coefficient k as the bifurcating parameter and applying central manifold and normal form analysis, it has been shown that the system is capable of Neimark–Sacker and flip bifurcations even without diffusion. Furthermore, with the influence of diffusion, the system exhibits pure Turing instability, Neimark–Sacker–Turing instability, and Flip–Turing instability. The numerical simulation section explores the path from bifurcation to chaos through calculations of the maximum Lyapunov exponent and the construction of a bifurcation diagram. The interconversion between different Turing instabilities is simulated by adjusting the timestep and self-diffusion coefficient values, which is based on pattern dynamics in ecological modeling. This contributes to a deeper understanding of the dynamic behaviors driven by aggregation effects in the host–parasitoid model. |
| format | Article |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-495de7fc55ff47afb26818f1c10fc3702025-01-10T13:18:19ZengMDPI AGMathematics2227-73902024-12-0113112510.3390/math13010125Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map LatticesShuo Liang0Wenlong Wang1Chunrui Zhang2Department of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaDepartment of Mathematics, Northeast Forestry University, Harbin 150040, ChinaHost–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasitoid, while the parasitoid depends on the host to complete its life cycle. This paper investigates the effect of parasitoid aggregation attacks on a host in a host–parasitoid model with self-diffusion on two-dimensional coupled map lattices. We assume that in the simulation of biological populations on a plane, the interactions between individuals follow periodic boundary conditions. The primary objective is to analyze the complex dynamics of the host–parasitoid interaction model induced by an aggregation effect and diffusion in a discrete setting. Using the aggregation coefficient k as the bifurcating parameter and applying central manifold and normal form analysis, it has been shown that the system is capable of Neimark–Sacker and flip bifurcations even without diffusion. Furthermore, with the influence of diffusion, the system exhibits pure Turing instability, Neimark–Sacker–Turing instability, and Flip–Turing instability. The numerical simulation section explores the path from bifurcation to chaos through calculations of the maximum Lyapunov exponent and the construction of a bifurcation diagram. The interconversion between different Turing instabilities is simulated by adjusting the timestep and self-diffusion coefficient values, which is based on pattern dynamics in ecological modeling. This contributes to a deeper understanding of the dynamic behaviors driven by aggregation effects in the host–parasitoid model.https://www.mdpi.com/2227-7390/13/1/125Neimark–Sacker bifurcationTuring instabilityflip bifurcationchaosFlip–Turing instabilityaggregation effect |
| spellingShingle | Shuo Liang Wenlong Wang Chunrui Zhang Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices Mathematics Neimark–Sacker bifurcation Turing instability flip bifurcation chaos Flip–Turing instability aggregation effect |
| title | Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices |
| title_full | Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices |
| title_fullStr | Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices |
| title_full_unstemmed | Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices |
| title_short | Pattern Dynamics Analysis of Host–Parasite Models with Aggregation Effect Based on Coupled Map Lattices |
| title_sort | pattern dynamics analysis of host parasite models with aggregation effect based on coupled map lattices |
| topic | Neimark–Sacker bifurcation Turing instability flip bifurcation chaos Flip–Turing instability aggregation effect |
| url | https://www.mdpi.com/2227-7390/13/1/125 |
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