ديناميكيات نموذج المفترس والفريسة تحت تأثير الانقاذ المتذبذب
محتوى المقالة الرئيسي
الملخص
تهدف هذه الورقة إلى دراسة فكرة جديدة تتضمن التحقيق في تأثير إنقاذ الفريسة مع تأثير التذبذب لاقتراح نموذج معدّل من مفترس -فريسة يشكل نموذجًا غير مستقل. ومع ذلك، يتم تحويل النموذج غير المستقل إلى نموذج مستقل بطريقة التقريب لتبسيط التحليل الرياضي واتباع السلوكيات الديناميكية. تمت دراسة بعض الخصائص النظرية للنموذج المستقل المقترح مثل المحدودية والاستقرار وظروف كولموغوروف. أظهرت النتائج التحليلية في هذا البحث أن السلوكيات الديناميكية مستقرة عموميا وأن تأثير الإنقاذ يزيد من إمكانية التعايش مقارنة بغير تأثير الإنقاذ. بالإضافة إلى ذلك، يتم تنفيذ عمليات المحاكاة العددية لإظهار تأثير الإنقاذ المتذبذب على ديناميكيات النموذج غير المستقل. تقدم النتائج التحليلية والرقمية نموذجًا أكثر تعايشا بين الفريسة والمفترس، وهذا يمكن أن يدعم أي نظام بيئي مهدد بالانقراض.
Received 17/1/2022, Revised 13/8/2022, Accepted 14/8/2022, Published Online First 20/2/2023
تفاصيل المقالة
هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.
كيفية الاقتباس
المراجع
Bassim SH, Sahar AK, Ahmed MA, Ahmed GA. Response of Green Lacewing Chrysoperla Carnea (Stephens) to Various Densities of Ephestia Cautella (Walk)Eggs. Baghdad Sci J. 2014; 11(3): 1094-9. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/1997
El-Saka HAA, Lee S, Jang B. Dynamic analysis of fractional-order predator-prey biological, economic System with Holling type II functional response. Nonlinear Dyn. 2019; 96(1): 407-416.
Wikan A, Kristensen O. Prey-Predator Interactions in Two and Three Species Population Models. Discrete Dyn Nat Soc. 2019; 2019: 1-14. https://doi.org/10.1155/2019/9543139
Alebraheem J. Paradox of Enrichment in a Stochastic Predator-Prey Model. Journal of Mathematics. 2020; 2020 : 1-8. https://doi.org/10.1155/2020/8864999
Alebraheem J. Relationship between the paradox of enrichment and the dynamics of persistence and extinction in prey-predator systems. Symmetry. 2018; 10(10): 1-18.
Alebraheem J, Yahya AH. Dynamics of a two predator–one prey system. Comp Appl Math. 2014; 33(3): 767-780.
Ghosh J, Sahoo B, Poria S. Prey-predator dynamics with prey refuge providing additional food to predator. Chaos Soliton Fract. 2017; 96(C): 110–119.
Banerjee M, Takeuchi Y. Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models. J Theor Biol. 2017; 2017(412): 154–171.
Ma Z, Wang S, Wang T, Tang H. Stability analysis of prey-predator System with Holling type functional response and prey refuge. Adv Differ Equ. 2017; 2017(243): 1-12.
Keong AT, Safuan HM, Jacob K. Dynamical behaviours of prey-predator fishery model with harvesting affected by toxic substances. Matematika. 2018; 34(1): 143–151.
Al-Moqbali M, Al-Salti N, Elmojtaba I. Prey–predator models with variable carrying capacity. Mathematics. 2018; 6(6): 1-12. https://doi.org/10.3390/math6060102
Naji RK. On The Dynamical Behavior of a Prey-Predator Model with the Effect of Periodic Forcing. Baghdad Sci J. 2007; 4(1): 147-157. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/779
Lotka AJ. Elements of Physical Biology. Nature. 1925; 1925: xxx+460.
Voltera V. Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Memorie della R. Acc. dei Lincei. 1926; 2(1926): 31-113.
Mishra P, Raw SN. Dynamical complexities in a predator-prey system involving teams of two prey and one predator. J Appl Math Comput. 2019; 61(2019): 1-24.
Mortoja SG, Panja P, Mondal SK. Dynamics of a predator-prey model with nonlinear incidence rate, Crowley-Martin type functional response and disease in prey population. Ecol Gen Genom. 2019; 10(2019): 100035.
Alidousti J, Ghafari E. Dynamic behavior of a fractional order prey-predator model with group defense. Chaos Soliton Fract. 2020; 134(C): 109688.
Deng H, Chen F, Zhu Z, Li Z. Dynamic behaviors of Lotka–Volterra predator–prey model incorporating predator cannibalism. Adv Differ Equ. 2019; 359(2019): 1-17. https://doi.org/10.1186/s13662-019-2289-8.
Rihan F, Alsakaji H, Rajivganthi C. Stability and Hopf Bifurcation of Three-Species Prey-Predator System with Time Delays and Allee Effect, Complexity, 2020; 2020: 1- 15 |Article ID 7306412 | https://doi.org/10.1155/2020/7306412
Alebraheem J, Nasser S Elazab, Mogtaba Mohammed, Anis Riahi, Ahmed Elmoasry, Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model. J Math. 2021; 2021: 1-11. Article ID 6611970,. https://doi.org/10.1155/2021/6611970
Alsakaji J, Kundu S, Rihan F. Delay differential model of one-predator two-prey System with Monod-Haldane and holling type II functional responses. Appl Math Comput. 2021; 397: 125919.
Fathalla A Rihan, Hebatallah J Alsakaji. Stochastic delay differential equations of three-species prey-predator System with cooperation among prey species. Discrete Contin Dyn Syst. 2022; 15 (2): 245-263. https://doi.org/10.3934/dcdss.2020468.
Rockwood LL. Introduction to population ecology. Cambridge Univ Press. 2006; 33(4): xi + 339.
Schenk D, Bacher S. Functional response of a generalist insect predator to one of its prey species in the field. J Anim Ecol. 2002; 71(3): 524–531.
Solomon ME. The natural control of animal populations. J Anim Ecol. 1949; 18(1): 1-35.
Holling CS. Some Characteristics of Simple Types of Predation and Parasitism. Can Entomol. 1959; 91(7): 385-398.
Louartassi Y, Alla A, Khalid H, Nabil A. Dynamics of a predator–prey model with harvesting and reserve area for prey in the presence of competition and toxicity. J Appl Math Comput. 2018; 1(2018): 305–321.
Lemnaouar MR, Khalfaoui M, Louartassi Y, Tolaimate I. Fractional Order Prey-Predator Model with Infected Predators in The Presence of Competition and Toxicity. Math Model Nat Phenom. 2020; 15(2020): 1-16.
Wang S, Yu H, Dai C, Zhao M. The Dynamical Behavior of a Predator-Prey System with Holling Type II Functional Response and Allee Effect. Appl Math. 2020; 11(05): 407-425. 10.4236/am.2020.115029.
Ian AM. Effects of temperature on growth of zooplankton, and the adaptive value of vertical migration. J Fish Res Board Can. 1963; 20(3): 685-727.
Glass NR. The effect of time of food deprivation on the routine oxygen consumption of largemouth black bass (Micropterus Salmoides). Ecology. 1968; 49(2): 1-4.
Arditi R, Abillon J, da Silva JV, The effect of a time-delay in a predator-prey model. Math Biosci. 1977; 33(1977): 107-120.
McArdle BH, Lawton J. Effects of prey-size and predator-instar on the predation of Daphnia by Notonecta. Ecol Entomol. 1979; 4(3): 267-275.
Yen J. Effects of prey concentration, prey size, predator life stage, predator starvation, and season on predation rates of the carnivorous copepod Euchaeta elongata. Mar Biol. 1983; 75(1983): 69-77.
Hethcote HW, Wang W, Han L, Ma Z. A predator–prey model with infected prey. Theor Popul Biol. 2004; 66(3): 259-268.
Alebraheem J. Fluctuations in interactions of prey predator systems. Sci Int (Lahore). 2016; 28(3): 2357-2362.
AlBasir F, Tiwari PK, Samanta S. Effects of incubation and gestation periods in a prey–predator model with infection in prey. Math Comput Simul. 2021; 190(C): 449-473. Available from: doi: 10.1016/j.matcom.2021.05.035
Alebraheem J. Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey. Diversity. 2021; 13(1): 1-21.
Van Schmidt ND, Beissinger SR. The rescue effect and inference from isolation–extinction relationships. Ecol Lett. 2020; 23(4): 598-606. Available from: 10.1111/ele.13460.
Eriksson A, Elı´as-Wolff F, Mehlig B, Manica A. The emergence of the rescue effect from explicit within-and between-patch dynamics in a metapopulation. Proc Biol Sci. 2014; 281(1780): 1-8.
Ovaskainen O. The interplay between immigration and local population dynamics in metapopulations. Ann Zool Fenn. 2017; 54(1): 113– 121.
Tahara T, Gavina MKA, Kawano T, Tubay JM, Rabajante JF, Ito H, et al. Asymptotic stability of a modified Lotka-Volterra model with small immigrations. Sci Rep. 2018; 8(7029): 1-7.
Bennett AA. Some algebraic analogies in matric theory. Ann Math. 1921; 23(1): 91-96.
Hasan AA. Modifying Some Iterative Methods for Solving Quadratic Eigenvalue Problems. Dissertation. MSc. Thesis, Wright State University, USA, 2017.
Sigmund K. Kolmogorov and population dynamics. In Kolmogorov's Heritage in Mathematics. Springer. Berlin. Heidelberg. 2007; 177-186.