Abstract
Recently the discrete fractional calculus (DFC) started to gain much importance due to its applications to the mathematical modeling of real world phenomena with memory effect. In this paper, the delayed logistic equation is discretized by utilizing the DFC approach and the related discrete chaos is reported. The Lyapunov exponent together with the discrete attractors and the bifurcation diagrams are given.
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Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (Grant No. 11301257), the Seed Funds for Major Science and Technology Innovation Projects of Sichuan Provincial Education Department (Grant No. 14CZ0026) and the Innovative Team Program of Sichuan Provincial Universities (Grant No. 13TD0001). The authors also thanks for the referees’ sincere and helpful suggestions to improve the work. One of the authors (G.C. Wu) feels grateful to Prof. Yu Xue for his important comments and remarks during the preliminary stage of writing this manuscript.
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Wu, GC., Baleanu, D. Discrete chaos in fractional delayed logistic maps. Nonlinear Dyn 80, 1697–1703 (2015). https://doi.org/10.1007/s11071-014-1250-3
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DOI: https://doi.org/10.1007/s11071-014-1250-3