Search results for "discrete fractional-order system"

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Coupled Discrete Fractional-Order Logistic Maps

2021

This paper studies a system of coupled discrete fractional-order logistic maps, modeled by Caputo’s delta fractional difference, regarding its numerical integration and chaotic dynamics. Some interesting new dynamical properties and unusual phenomena from this coupled chaotic-map system are revealed. Moreover, the coexistence of attractors, a necessary ingredient of the existence of hidden attractors, is proved and analyzed.

General Mathematicscaputo delta fractional differenceChaoticattraktoritstabilityStability (probability)fractional-order difference equationNumerical integrationNonlinear Sciences::Chaotic DynamicsAttractorQA1-939Computer Science (miscellaneous)Applied mathematicsOrder (group theory)dynaamiset systeemitEngineering (miscellaneous)Mathematicsdiscrete fractional-order systemhidden attractorMathematicsMathematics
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D3 Dihedral Logistic Map of Fractional Order

2021

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

kaaosteoriaGeneral Mathematicscomputational_mathematicscaputo delta fractional differencedihedral symmetry <i>D</i><sub>3</sub>attraktoritmatemaattinen analyysiNonlinear Sciences::Chaotic DynamicsbifurkaatioQA1-939Computer Science (miscellaneous)dihedral symmetry D3dynaamiset systeemitEngineering (miscellaneous)Mathematicsdiscrete fractional-order systemdiscrete fractional-order system; caputo delta fractional difference; hidden attractor; dihedral symmetry <i>D</i><sub>3</sub>hidden attractor
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