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Synchronous Dynamics and Bifurcation Analysis in Two Delay Coupled Oscillators with Recurrent Inhibitory Loops

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Abstract

In this study, the dynamics and low-codimension bifurcation of the two delay coupled oscillators with recurrent inhibitory loops are investigated. We discuss the absolute synchronization character of the coupled oscillators. Then the characteristic equation of the linear system is examined, and the possible low-codimension bifurcations of the coupled oscillator system are studied by regarding eigenvalues of the connection matrix as bifurcation parameter, and the bifurcation diagram in the γ–ρ plane is obtained. Applying normal form theory and the center manifold theorem, the stability and direction of the codimension bifurcations are determined. Moreover, the symmetric bifurcation theory and representation theory of Lie groups are used to investigate the spatio-temporal patterns of the periodic oscillations. Finally, numerical results are applied to illustrate the results obtained.

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Acknowledgements

The study was supported in the part by the National Natural Science Foundation of China (Grant No. 10972073, 11032004) and New Century Excellent Talents in University (NCET-09-0335).

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Authors and Affiliations

  1. College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, PR China

    Lianhua Wang, Yiming Jin & Jianjun Ma

  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan, 410082, PR China

    Jian Peng

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  1. Lianhua Wang
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  2. Jian Peng
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  3. Yiming Jin
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  4. Jianjun Ma
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Correspondence to Lianhua Wang.

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Communicated by P. Newton.

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Wang, L., Peng, J., Jin, Y. et al. Synchronous Dynamics and Bifurcation Analysis in Two Delay Coupled Oscillators with Recurrent Inhibitory Loops. J Nonlinear Sci 23, 283–302 (2013). https://doi.org/10.1007/s00332-012-9151-4

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  • DOI: https://doi.org/10.1007/s00332-012-9151-4

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