Fractional <i>q</i>-deformed chaotic maps: A weight function approach
Guo–Cheng Wu, Mehmet Niyazi Çankaya, Santo Banerjee
Abstract
The fractional derivative holds long-time memory effects or non-locality. It successfully depicts the dynamical systems with long-range interactions. However, it becomes challenging to investigate chaos in the deformed fractional discrete-time systems. This study turns to fractional quantum calculus on the time scale and reports chaos in fractional q-deformed maps. The discrete memory kernels are used, and a weight function approach is proposed for fractional modeling. Rich q-deformed dynamics are demonstrated, which shows the methodology's efficiency.
Topics & Concepts
Fractional calculusChaoticFunction (biology)LocalityRange (aeronautics)MathematicsScale (ratio)Statistical physicsApplied mathematicsComputer sciencePhysicsQuantum mechanicsArtificial intelligenceMaterials scienceBiologyEvolutionary biologyLinguisticsPhilosophyComposite materialFractional Differential Equations SolutionsQuantum chaos and dynamical systemsChaos control and synchronization