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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 9724139, 13 pages
http://dx.doi.org/10.1155/2016/9724139
Research Article

Border Collision Bifurcations in a Generalized Model of Population Dynamics

1Department of Mathematics and Physics, University of Los Llanos, 500001 Villavicencio, Colombia
2Department of Economics and Law, University of Macerata, 62100 Macerata, Italy
3Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain

Received 21 December 2015; Revised 24 February 2016; Accepted 22 March 2016

Academic Editor: Xiaohua Ding

Copyright © 2016 Lilia M. Ladino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, NY, USA, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  2. F. Balibrea, A. Martinez, and J. C. Valverde, “Local bifurcations of continuous dynamical systems under higher order conditions,” Applied Mathematics Letters, vol. 23, no. 3, pp. 230–234, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. Yuan, W. Jiang, and Y. Wang, “Saddle-node-Hopf bifurcation in a modified Leslie-Gower predator-prey model with time-delay and prey harvesting,” Journal of Mathematical Analysis and Applications, vol. 422, no. 2, pp. 1072–1090, 2015. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. D. Franco and J. Perán, “Stabilization of population dynamics via threshold harvesting strategies,” Ecological Complexity, vol. 14, pp. 85–94, 2013. View at Publisher · View at Google Scholar · View at Scopus
  5. D. J. W. Simpson, Bifurcations in Piecewise-Smooth Continuous Systems, vol. 70 of Nonlinear Science Series A, World Scientific, New Jersey, NJ, USA, 2010.
  6. M. I. Feigin, “Doubling of the oscillation period with C-bifurcations in piecewise continuous systems,” Journal of Applied Mathematics and Mechanics (PMM), vol. 34, pp. 861–869, 1970. View at Google Scholar
  7. M. Di Bernardo, M. I. Feigin, S. J. Hogan, and M. E. Homer, “Local analysis of C-bifurcations in ndimensional piecewise-smooth dynamical systems,” Chaos, Solitons and Fractals, vol. 10, no. 11, pp. 1881–1908, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. E. Nusse and J. A. Yorke, “Border-collision bifurcations including ‘period two to period three’ for piecewise smooth systems,” Physica D: Nonlinear Phenomena, vol. 57, no. 1-2, pp. 39–57, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. Brianzoni, E. Michetti, and I. Sushko, “Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map,” Mathematics and Computers in Simulation, vol. 81, no. 1, pp. 52–61, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. D. J. Simpson and J. D. Meiss, “Aspects of bifurcation theory for piecewise-smooth, continuous systems,” Physica D: Nonlinear Phenomena, vol. 241, no. 22, pp. 1861–1868, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. Agliari, P. Commendatore, I. Foroni, and I. Kubin, “Border collision bifurcations in a footloose capital model with first nature firms,” Computational Economics, vol. 38, no. 3, pp. 349–366, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. L. M. Ladino, C. Mammana, E. Michetti, and J. C. Valverde, “Discrete time population dynamics of a two-stage species with recruitment and capture,” Chaos, Solitons & Fractals, vol. 85, pp. 143–150, 2015. View at Publisher · View at Google Scholar
  13. L. M. Ladino and J. C. Valverde, “Population dynamics of a two-stage species with recruitment,” Mathematical Methods in the Applied Sciences, vol. 36, no. 6, pp. 722–729, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. CCI and INCODER, Pesca y Acuicultura Colombia 2006, Coorporación Colombiana Internacional CCI. Instituto Colombiano de Desarrollo Rural INCODER, Bogotá, Colombia, 2006.
  15. I. Kubin and L. Gardini, “Border collision bifurcations in boom and bust cycles,” Journal of Evolutionary Economics, vol. 23, no. 4, pp. 811–829, 2013. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Banerjee and C. Grebogi, “Border collision bifurcations in two-dimensional piecewise smooth maps,” Physical Review E, vol. 59, no. 4, pp. 4052–4061, 1999. View at Google Scholar · View at Scopus
  17. D. J. Simpson, “On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations,” Applied Mathematics Letters, vol. 38, pp. 162–167, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H. E. Nusse and J. A. Yorke, “Border-collision bifurcations for piecewise smooth one-dimensional maps,” International Journal of Bifurcation and Chaos, vol. 5, no. 1, pp. 189–207, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  19. I. Sushko, L. Gardini, and T. Puu, “Regular and chaotic growth in a Hicksian floor/ceiling model,” Journal of Economic Behavior and Organization, vol. 75, no. 1, pp. 77–94, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. A. Medio and M. Lines, Nonlinear Dynamics: A Primer, Cambridge University Press, Cambridge, UK, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. Radi, L. Gardini, and V. Avrutin, “The role of constraints in a segregation model: the symmetric case,” Chaos, Solitons & Fractals, vol. 66, pp. 103–119, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. L. Gardini, D. Fournier-Prunaret, and P. ChargéP, “Border collision bifurcations in a two-dimensional piecewise smooth map from a simple switching circuit,” Chaos, vol. 21, no. 2, Article ID 023106, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus