Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2023, Cilt: 5 Sayı: 3, 207 - 218, 30.11.2023
https://doi.org/10.51537/chaos.1357543

Öz

Proje Numarası

For this particular research, no specific funding has been allocated.

Kaynakça

  • Abarbanel, H. D. I., 1996 Analysis of Observed Chaotic Data. Number 34, Springer New York, NY.
  • Alaydi, S., 1996 An introduction to difference equations. Number 32, Springer New York, NY.
  • Chen, Y. and S. Changming, 2008 Stability and hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay. Chaos, Solitons & Fractals 38: 1104–1114.
  • Fazly, M. and M. Hesaaraki, 2007 Periodic solutions for a discrete time predator–prey system with monotone functional responses. Comptes Rendus. Mathématique 345: 199–202.
  • Gakkhar, S. and A. Singh, 2012 Complex dynamics in a prey predator system with multiple delays. Communications in Nonlinear Science and Numerical Simulation 17: 914–929.
  • Garic Demirovic M., K. M. . N. M., 2009 Global behavior of four competitive rational systems of difference equations in the plane. Discrete Dynamics in Nature and Society 2009: 153058–153092.
  • Hu Z., T. Z. . Z., 2011 Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response. Nonlinear Analysis: Real World Applications 12(4): 2356–2377.
  • Ibrahim, T. F. and N. Touafek, 2014 Max-type system of difference equations with positive two-periodic sequences. Math. methods Appl. sci 37: 2562–2569.
  • Joydip Dhar, H. S. . H. S. B., 2015 Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey. Applied Mathematics and Computation 252: 1104–1114.
  • Kalabusic S., K. M. . P. E., 2011 Multiple attractors for a competitive system of rational difference equations in the plane. Abstract and Applied Analysis 37(16): 1–17.
  • Khan, A., 2016 Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model. SpringerPlus 5: 121–126.
  • L. Men, G.W. Z.W. L. .W. L., B. S. Chen, 2015 Hopf bifurcation and nonlinear state feedback control for a modified Lotka-Volterra differential algebraic predator-prey system. Fifth International Conference on Intelligent Control and Information Processing 2015: 233–238.
  • Pan, S. X., 2013 Asymptotic spreading in a Lotka-Volterra predatorprey system. The Journal of Mathematical Analysis and Applications 407: 230–236.
  • Q., Q. M. . K. A., 2015 Periodic solutions for discrete time predatorprey system with monotone functional responses. International Academy of Ecology and Environmental Sciences 5(1): 48–62.
  • R. M. Eide, N. T. F. . R. A. V. G., A. L. Krause, 2018 The origins and evolutions of predator-prey theory. Journal of Theoretical Biology 451: 19–34.
  • Rana, S., U. Kulsum, et al., 2017 Bifurcation analysis and chaos control in a discrete-time predator-prey system of leslie type with simplified holling type iv functional response. Discrete Dynamics in Nature and Society 2017.
  • Salman SM, Y. A. . E. A., 2016 Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response. Chaos Solitons Fractals 93: 20–31.
  • Sen M, B. M. . M. A., 2012 Bifurcation analysis of a ratio-dependent prey-predator model with the Allee effect. Ecological Complexity 11: 12–27.
  • Singh, A. and P. Deolia, 2020 Dynamical analysis and chaos control in discrete-time prey-predator model. Communications in Nonlinear Science and Numerical Simulation 90: 105313.
  • Smith, J. M., 1968 Mathematical Ideas in Biology, volume 1. Cambridge University Press.
  • X. W. Jiang, T. W. H. . H. C. Y., X. Y. Chen, 2021 Bifurcation and control for a predator-prey system with two delays. IEEE Trans-actions on Circuits and Systems II: Express Briefs 68: 376–380.
  • X. Zhang, Z. W. . T. Z., 2016 Periodic solutions for discrete time predator-prey system with monotone functional responses. Journal of Biological Dynamics 10: 1–17.
  • Z. L. Luo, Y. P. L. . Y. X. D., 2016 Rank one chaos in periodically kicked Lotka-Volterra predator-prey system with time delay. Nonlinear Dynamics 85: 797–811.
  • Zhang C.H, Y. X. . C. G., 2010 Hopf bifurcations in a predator-prey system with a discrete delay and a distributed delay. Nonlinear Anal Real World Application 10: 4141–4153.
  • Zu, L., D. Jiang, D. O’Regan, T. Hayat, and B. Ahmad, 2018 Ergodic property of a lotka–volterra predator–prey model with white noise higher order perturbation under regime switching. Applied Mathematics and Computation 330: 93–102.

Analyzing Predator-Prey Interaction in Chaotic and Bifurcating Environments

Yıl 2023, Cilt: 5 Sayı: 3, 207 - 218, 30.11.2023
https://doi.org/10.51537/chaos.1357543

Öz

An analysis of discrete-time predator-prey systems is presented in this paper by determining the minimum amount of prey consumed before predators reproduce, as well as by analyzing the system's stability and bifurcation. In order to investigate the local stability of the interior equilibrium point of the proposed model, discrete dynamics system theory is employed first. Moreover, the characteristic equation is analyzed to determine the Neimark-Sacker bifurcation of the system. The normal form and bifurcation theory are used to investigate the NS bifurcation around the interior equilibrium point. Based on its analysis, the system exhibits Neimark-Sacker bifurcation when positive parameters are present and non-negative conditions are met. Develop a feedback control strategy to discover the region of stability of the chaotic behavior. By utilizing the maximum laypanuou exponent, the effect of initial conditions on developed systems is further explored. Finally, a computer simulation illustrates the results of the analysis.

Etik Beyan

It has been reported that none of the authors have any conflicts of interest.

Proje Numarası

For this particular research, no specific funding has been allocated.

Kaynakça

  • Abarbanel, H. D. I., 1996 Analysis of Observed Chaotic Data. Number 34, Springer New York, NY.
  • Alaydi, S., 1996 An introduction to difference equations. Number 32, Springer New York, NY.
  • Chen, Y. and S. Changming, 2008 Stability and hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay. Chaos, Solitons & Fractals 38: 1104–1114.
  • Fazly, M. and M. Hesaaraki, 2007 Periodic solutions for a discrete time predator–prey system with monotone functional responses. Comptes Rendus. Mathématique 345: 199–202.
  • Gakkhar, S. and A. Singh, 2012 Complex dynamics in a prey predator system with multiple delays. Communications in Nonlinear Science and Numerical Simulation 17: 914–929.
  • Garic Demirovic M., K. M. . N. M., 2009 Global behavior of four competitive rational systems of difference equations in the plane. Discrete Dynamics in Nature and Society 2009: 153058–153092.
  • Hu Z., T. Z. . Z., 2011 Stability and bifurcation analysis of a discrete predator-prey model with nonmonotonic functional response. Nonlinear Analysis: Real World Applications 12(4): 2356–2377.
  • Ibrahim, T. F. and N. Touafek, 2014 Max-type system of difference equations with positive two-periodic sequences. Math. methods Appl. sci 37: 2562–2569.
  • Joydip Dhar, H. S. . H. S. B., 2015 Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey. Applied Mathematics and Computation 252: 1104–1114.
  • Kalabusic S., K. M. . P. E., 2011 Multiple attractors for a competitive system of rational difference equations in the plane. Abstract and Applied Analysis 37(16): 1–17.
  • Khan, A., 2016 Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model. SpringerPlus 5: 121–126.
  • L. Men, G.W. Z.W. L. .W. L., B. S. Chen, 2015 Hopf bifurcation and nonlinear state feedback control for a modified Lotka-Volterra differential algebraic predator-prey system. Fifth International Conference on Intelligent Control and Information Processing 2015: 233–238.
  • Pan, S. X., 2013 Asymptotic spreading in a Lotka-Volterra predatorprey system. The Journal of Mathematical Analysis and Applications 407: 230–236.
  • Q., Q. M. . K. A., 2015 Periodic solutions for discrete time predatorprey system with monotone functional responses. International Academy of Ecology and Environmental Sciences 5(1): 48–62.
  • R. M. Eide, N. T. F. . R. A. V. G., A. L. Krause, 2018 The origins and evolutions of predator-prey theory. Journal of Theoretical Biology 451: 19–34.
  • Rana, S., U. Kulsum, et al., 2017 Bifurcation analysis and chaos control in a discrete-time predator-prey system of leslie type with simplified holling type iv functional response. Discrete Dynamics in Nature and Society 2017.
  • Salman SM, Y. A. . E. A., 2016 Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response. Chaos Solitons Fractals 93: 20–31.
  • Sen M, B. M. . M. A., 2012 Bifurcation analysis of a ratio-dependent prey-predator model with the Allee effect. Ecological Complexity 11: 12–27.
  • Singh, A. and P. Deolia, 2020 Dynamical analysis and chaos control in discrete-time prey-predator model. Communications in Nonlinear Science and Numerical Simulation 90: 105313.
  • Smith, J. M., 1968 Mathematical Ideas in Biology, volume 1. Cambridge University Press.
  • X. W. Jiang, T. W. H. . H. C. Y., X. Y. Chen, 2021 Bifurcation and control for a predator-prey system with two delays. IEEE Trans-actions on Circuits and Systems II: Express Briefs 68: 376–380.
  • X. Zhang, Z. W. . T. Z., 2016 Periodic solutions for discrete time predator-prey system with monotone functional responses. Journal of Biological Dynamics 10: 1–17.
  • Z. L. Luo, Y. P. L. . Y. X. D., 2016 Rank one chaos in periodically kicked Lotka-Volterra predator-prey system with time delay. Nonlinear Dynamics 85: 797–811.
  • Zhang C.H, Y. X. . C. G., 2010 Hopf bifurcations in a predator-prey system with a discrete delay and a distributed delay. Nonlinear Anal Real World Application 10: 4141–4153.
  • Zu, L., D. Jiang, D. O’Regan, T. Hayat, and B. Ahmad, 2018 Ergodic property of a lotka–volterra predator–prey model with white noise higher order perturbation under regime switching. Applied Mathematics and Computation 330: 93–102.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Biyomedikal Mühendisliği (Diğer)
Bölüm Research Articles
Yazarlar

Ansar Abbas 0000-0003-4316-3574

Abdul Khaliq 0000-0001-8802-9200

Proje Numarası For this particular research, no specific funding has been allocated.
Yayımlanma Tarihi 30 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 5 Sayı: 3

Kaynak Göster

APA Abbas, A., & Khaliq, A. (2023). Analyzing Predator-Prey Interaction in Chaotic and Bifurcating Environments. Chaos Theory and Applications, 5(3), 207-218. https://doi.org/10.51537/chaos.1357543

Chaos Theory and Applications in Applied Sciences and Engineering: An interdisciplinary journal of nonlinear science 23830 28903   

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