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Higher-codimension bifurcations caused by delay

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Abstract

In this paper, we give a detailed study of rich dynamics in two-parameter families of two-dimensional generalized delayed discrete Cournot duopoly models. Multistability, such as the coexistence of period-2/quasiperiodic (limit-cycle), chaotic/regular motions or synchronized/asynchronized solutions are discussed. Complexity caused by delay, including the change of local stability regions and the occurrence of higher-codimension bifurcations, is to be discovered.

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References

  1. Guo, S., Tang, X., Huang, L.: Bifurcation analysis in a discrete-time single-directional network with delays. Neurocomputing 71(79), 1422–1435 (2008)

    Article  Google Scholar 

  2. Guo, S., Tang, X., Huang, L.: Stability and bifurcation in a discrete system of two neurons with delays. Nonlinear Anal., Real World Appl. 9(4), 1323–1335 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hassard, B.D., Kazarinoff, N.D., Wan, Y.H.: Theory and Applications of Hopf Bifurcation. London Mathematical Society Lecture Note Series, vol. 41. Cambridge University Press, Cambridge (1981)

    MATH  Google Scholar 

  4. Kuruklis, S.A.: The asymptotic stability of x n+1−ax n +bx n−k =0. J. Math. Anal. Appl. 188, 719–731 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (1995)

    MATH  Google Scholar 

  6. Marotto, F.R.: Snap-back repellers imply chaos in ℝn. J. Math. Anal. Appl. 63, 199–223 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  7. Peng, M., Huang, L., Wang, G.: Higher-codimension bifurcations in a discrete unidirectional neural network model with delayed feedback. Chaos 18, 023105 (2008)

    Article  MathSciNet  Google Scholar 

  8. Peng, M., Jiang, Z., Jiang, X., Hu, J., Qu, Y.: Multistability and complex dynamics in a simple discrete economic model. Chaos Solitons Fractals (2009, in press)

  9. Wang, G., Peng, M.: Rich oscillation patterns in a simple delayed neuron network and its linear control. Int. J. Bifurc. Chaos Appl. Sci. Eng. (2009, in press)

  10. Peng, M., Yuan, Y.: Synchronization and desynchronization in a delayed discrete neural network. Int. J. Bifurc. Chaos Appl. Sci. Eng. 17(3), 781–803 (2007)

    Article  MathSciNet  Google Scholar 

  11. Wu, J., Zhang, R.: A simple delayed network with large capacity for associate memory. Discrete Control Dyn. Syst. B 4, 853–865 (2004)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiao Tong University, Beijing, 100044, China

    Mingshu Peng

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Rong Yuan

Authors
  1. Mingshu Peng
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  2. Rong Yuan
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Corresponding author

Correspondence to Mingshu Peng.

Additional information

Support partially by NSFC(10871019), SRF for ROCS, SEM, Scientific Research Foundation of Beijing Jiao Tong University (2007XM050) (M. Peng), NSFC and RFDP (R. Yuan).

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Peng, M., Yuan, R. Higher-codimension bifurcations caused by delay. Nonlinear Dyn 58, 453–467 (2009). https://doi.org/10.1007/s11071-009-9492-1

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  • DOI: https://doi.org/10.1007/s11071-009-9492-1

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