{"title":"基于自我记忆的扩散对捕食者-猎物模型的影响","authors":"Yunzhuo Zhang, Xuebing Zhang, Shunjie Li","doi":"10.1007/s00033-024-02256-1","DOIUrl":null,"url":null,"abstract":"<p>In this research, we examine a diffusive predator–prey model with spatial memory. We begin by checking that the suggested model has a unique solution that is boundedness. The stability of each equilibrium is then examined. Local and global stability as well as bifurcations are investigated in the non-delayed model at stationary equilibrium. Then, we investigate the Hopf bifurcation using the delay as the bifurcation parameter. In order to back up our theoretical findings, we then give some numerical simulations.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The effect of self-memory-based diffusion on a predator–prey model\",\"authors\":\"Yunzhuo Zhang, Xuebing Zhang, Shunjie Li\",\"doi\":\"10.1007/s00033-024-02256-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this research, we examine a diffusive predator–prey model with spatial memory. We begin by checking that the suggested model has a unique solution that is boundedness. The stability of each equilibrium is then examined. Local and global stability as well as bifurcations are investigated in the non-delayed model at stationary equilibrium. Then, we investigate the Hopf bifurcation using the delay as the bifurcation parameter. In order to back up our theoretical findings, we then give some numerical simulations.</p>\",\"PeriodicalId\":501481,\"journal\":{\"name\":\"Zeitschrift für angewandte Mathematik und Physik\",\"volume\":\"15 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-024-02256-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02256-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The effect of self-memory-based diffusion on a predator–prey model
In this research, we examine a diffusive predator–prey model with spatial memory. We begin by checking that the suggested model has a unique solution that is boundedness. The stability of each equilibrium is then examined. Local and global stability as well as bifurcations are investigated in the non-delayed model at stationary equilibrium. Then, we investigate the Hopf bifurcation using the delay as the bifurcation parameter. In order to back up our theoretical findings, we then give some numerical simulations.
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