{"title":"非线性时滞生态模型的全局稳定性分析与数值模拟","authors":"M.ISMAIL ABDELRAHMAN, ASHRAF A. GOUDA","doi":"10.58675/2636-3305.1631","DOIUrl":null,"url":null,"abstract":"Discrete models are particularly useful for modelling population dynamics when the population size remains small over several generations or when it is relatively constant within a single generation. We focus on finding effective solutions to the challenges posed by such populations. In our research, we have successfully used qualitative analytic techniques to study a three species model. It is important to consider the reproductive process and other population dynamics as happening in real-time, even for species with unclear reproductive seasons. While the delay technique has introduced some complexities, we have identified sufficient conditions to address them. Our study examines the global stability of a three species ecological model that does not consider delayed intraspecific competition. We analyze a delayed Lotka Volterra system, which demonstrates global stability when the interaction matrix is effective. We present numerical simulations to illustrate the theoretical results of the delay differential equation. Since delay differential equation models are always challenging to solve, we propose the use of JiTCDDE (just-in-time compilation for delay differential equations) of the DDE integration method to solve the dynamical three species models.","PeriodicalId":7687,"journal":{"name":"Al-Azhar Bulletin of Science","volume":"98 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Stability Analysis And Numerical Simulation For Nonlinear Ecological Model With Delay\",\"authors\":\"M.ISMAIL ABDELRAHMAN, ASHRAF A. GOUDA\",\"doi\":\"10.58675/2636-3305.1631\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Discrete models are particularly useful for modelling population dynamics when the population size remains small over several generations or when it is relatively constant within a single generation. We focus on finding effective solutions to the challenges posed by such populations. In our research, we have successfully used qualitative analytic techniques to study a three species model. It is important to consider the reproductive process and other population dynamics as happening in real-time, even for species with unclear reproductive seasons. While the delay technique has introduced some complexities, we have identified sufficient conditions to address them. Our study examines the global stability of a three species ecological model that does not consider delayed intraspecific competition. We analyze a delayed Lotka Volterra system, which demonstrates global stability when the interaction matrix is effective. We present numerical simulations to illustrate the theoretical results of the delay differential equation. Since delay differential equation models are always challenging to solve, we propose the use of JiTCDDE (just-in-time compilation for delay differential equations) of the DDE integration method to solve the dynamical three species models.\",\"PeriodicalId\":7687,\"journal\":{\"name\":\"Al-Azhar Bulletin of Science\",\"volume\":\"98 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Al-Azhar Bulletin of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.58675/2636-3305.1631\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Al-Azhar Bulletin of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.58675/2636-3305.1631","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
当种群规模在几代内保持较小或在一代内相对恒定时,离散模型对于建模种群动态特别有用。我们的重点是寻找有效的解决办法,以应对这些人口构成的挑战。在我们的研究中,我们成功地使用了定性分析技术来研究三种模型。重要的是要考虑到生殖过程和其他种群动态是实时发生的,即使对生殖季节不明确的物种也是如此。虽然延迟技术引入了一些复杂性,但我们已经确定了解决这些问题的充分条件。我们的研究考察了一个不考虑延迟种内竞争的三物种生态模型的全局稳定性。我们分析了一个时滞Lotka Volterra系统,证明了当交互矩阵有效时系统是全局稳定的。我们给出了数值模拟来说明延迟微分方程的理论结果。针对时滞微分方程模型求解难度较大的问题,提出了采用jit -in-time compilation for delay differential equations的DDE积分方法求解动态三种模型。
Global Stability Analysis And Numerical Simulation For Nonlinear Ecological Model With Delay
Discrete models are particularly useful for modelling population dynamics when the population size remains small over several generations or when it is relatively constant within a single generation. We focus on finding effective solutions to the challenges posed by such populations. In our research, we have successfully used qualitative analytic techniques to study a three species model. It is important to consider the reproductive process and other population dynamics as happening in real-time, even for species with unclear reproductive seasons. While the delay technique has introduced some complexities, we have identified sufficient conditions to address them. Our study examines the global stability of a three species ecological model that does not consider delayed intraspecific competition. We analyze a delayed Lotka Volterra system, which demonstrates global stability when the interaction matrix is effective. We present numerical simulations to illustrate the theoretical results of the delay differential equation. Since delay differential equation models are always challenging to solve, we propose the use of JiTCDDE (just-in-time compilation for delay differential equations) of the DDE integration method to solve the dynamical three species models.