Abstract
In this paper, a class of time fractional Cohen–Grossberg neural networks with time delays in leakage terms and diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation are established. By using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulae are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main theoretical results.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (Nos. 11371368, 11071254, 61305076), the Natural Science Foundation of Hebei Province of China (No. A2014506015) and the Natural Science Foundation for Young Scientists of Hebei Province (No. A2013506012).
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Tian, X., Xu, R. Stability and Hopf Bifurcation of Time Fractional Cohen–Grossberg Neural Networks with Diffusion and Time Delays in Leakage Terms. Neural Process Lett 45, 593–614 (2017). https://doi.org/10.1007/s11063-016-9544-8
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DOI: https://doi.org/10.1007/s11063-016-9544-8