Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 57, Issue -, Pages 352-358Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.10.009
Keywords
Chaos; Bifurcation; Logistic map; Discrete fractional map
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Funding
- National Natural Science Foundation of China [11401405, 61701329, 11501386]
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The fractional-order discrete maps with chaotic behaviors based on the theory of fractional difference are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps. (C) 2017 Elsevier B.V. All rights reserved.
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