Analysis of a Class of Predation-Predation Model Dynamics with Random Perturbations
In this paper, we study a class of predation–prey biological models with random perturbation. Firstly, the existence and uniqueness of systematic solutions can be proven according to Lipschitz conditions, and then we prove that the systematic solution exists globally. Moreover, the article discusses...
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Published in | Mathematics (Basel) Vol. 10; no. 18; p. 3238 |
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Abstract | In this paper, we study a class of predation–prey biological models with random perturbation. Firstly, the existence and uniqueness of systematic solutions can be proven according to Lipschitz conditions, and then we prove that the systematic solution exists globally. Moreover, the article discusses the long-term dynamical behavior of the model, which studies the stationary distribution and gradual properties of the system. Next, we use two different methods to give the conditions of population extinction. From what has been discussed above, we can safely draw the conclusion that our results are reasonable by using numerical simulation. |
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AbstractList | In this paper, we study a class of predation–prey biological models with random perturbation. Firstly, the existence and uniqueness of systematic solutions can be proven according to Lipschitz conditions, and then we prove that the systematic solution exists globally. Moreover, the article discusses the long-term dynamical behavior of the model, which studies the stationary distribution and gradual properties of the system. Next, we use two different methods to give the conditions of population extinction. From what has been discussed above, we can safely draw the conclusion that our results are reasonable by using numerical simulation. |
Audience | Academic |
Author | Tan, Xuewen Luo, Wenhui Chen, Hui Liu, Pengpeng |
Author_xml | – sequence: 1 givenname: Xuewen surname: Tan fullname: Tan, Xuewen – sequence: 2 givenname: Pengpeng surname: Liu fullname: Liu, Pengpeng – sequence: 3 givenname: Wenhui surname: Luo fullname: Luo, Wenhui – sequence: 4 givenname: Hui surname: Chen fullname: Chen, Hui |
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Cites_doi | 10.3934/math.2021715 10.1088/1751-8121/ac654f 10.1186/s13662-020-02868-7 10.1051/mmnp/20149305 10.1007/s00285-016-1010-8 10.1080/10236198.2021.1945047 10.3390/fractalfract6010034 10.1155/2011/376862 10.1016/S0022-247X(03)00464-5 10.3934/math.2020234 10.1073/pnas.1318122111 10.1016/0020-0190(93)90029-9 10.1515/ijnsns-2019-0255 10.1103/PhysRevE.104.014121 10.1080/07362994.2021.1944876 10.1007/s11118-018-9681-y 10.1098/rspa.2003.1221 10.3934/math.2020189 10.1103/PhysRevE.93.062411 10.1007/s40840-020-00967-y 10.1080/00207160.2019.1618846 10.1134/S0012266122030107 10.1016/j.jmaa.2014.03.049 10.1016/S0252-9602(13)60047-8 10.1103/PhysRevE.106.044113 10.1103/PhysRevE.103.012122 10.1016/j.plrev.2015.01.004 10.3934/math.2021355 10.1073/pnas.2017463118 10.3390/fractalfract6060339 |
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SubjectTerms | Biological models (mathematics) Biology Brownian motion Food science gradual properties Lipschitz conditions Mathematical models Mathematics numerical simulation Perturbation Perturbation (Mathematics) Population population extinction Predation Predation (Biology) random perturbation stationary distribution |
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