{"title":"具有求学行为和斯密增长的扩散捕食者-猎物模型中的图灵-霍普夫分岔","authors":"","doi":"10.1016/j.aml.2024.109257","DOIUrl":null,"url":null,"abstract":"<div><p>This paper explores the dynamics of a diffusive predator–prey model, considering schooling behavior and Smith growth in prey. Initially, we have formulated the pertinent characteristic equations. Subsequently, We proceed to examine the existence of the Turing bifurcation and Hopf bifurcation, phenomena that describe the emergence of spatial and temporal patterns due to diffusion and oscillations, respectively, and focusing on the parameters of the intrinsic growth rate <span><math><mi>γ</mi></math></span> and the diffusion coefficient <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of the prey. Finally, we conduct numerical simulations to validate our theoretical findings and further illustrate the dynamics of the predator–prey system, considering schooling behavior and Smith growth in prey.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Turing–Hopf bifurcation in a diffusive predator–prey model with schooling behavior and Smith growth\",\"authors\":\"\",\"doi\":\"10.1016/j.aml.2024.109257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper explores the dynamics of a diffusive predator–prey model, considering schooling behavior and Smith growth in prey. Initially, we have formulated the pertinent characteristic equations. Subsequently, We proceed to examine the existence of the Turing bifurcation and Hopf bifurcation, phenomena that describe the emergence of spatial and temporal patterns due to diffusion and oscillations, respectively, and focusing on the parameters of the intrinsic growth rate <span><math><mi>γ</mi></math></span> and the diffusion coefficient <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> of the prey. Finally, we conduct numerical simulations to validate our theoretical findings and further illustrate the dynamics of the predator–prey system, considering schooling behavior and Smith growth in prey.</p></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924002775\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924002775","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Turing–Hopf bifurcation in a diffusive predator–prey model with schooling behavior and Smith growth
This paper explores the dynamics of a diffusive predator–prey model, considering schooling behavior and Smith growth in prey. Initially, we have formulated the pertinent characteristic equations. Subsequently, We proceed to examine the existence of the Turing bifurcation and Hopf bifurcation, phenomena that describe the emergence of spatial and temporal patterns due to diffusion and oscillations, respectively, and focusing on the parameters of the intrinsic growth rate and the diffusion coefficient of the prey. Finally, we conduct numerical simulations to validate our theoretical findings and further illustrate the dynamics of the predator–prey system, considering schooling behavior and Smith growth in prey.
期刊介绍:
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.