Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems

Bhalekar, Sachin; Gade, Prashant M.

doi:10.1007/s00332-023-09978-y

J Nonlinear Sci

2023

DOI: 10.1007/s00332-023-09978-y

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Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems

Sachin Bhalekar,

Prashant M. Gade

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2024

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Cited by 4 publications

References 40 publications

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Bidirectional coupling in fractional order maps of incommensurate orders

Bhalekar,

Gade,

Joshi

2024

Chaos, Solitons & Fractals

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Bidirectional coupling in fractional order maps of incommensurate orders

Bhalekar,

Gade,

Joshi

2024

Chaos, Solitons & Fractals

View full text Add to dashboard Cite

Periodic Points, Stability, Bifurcations, and Transition to Chaos in Generalized Fractional Maps

Edelman

2024

IFAC-PapersOnLine

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Stability analysis of fractional difference equations with delay

Joshi,

Bhalekar,

Gade

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the “fractional order difference,” can also have a long-time memory. Therefore, the fractional difference equations with delay are an appropriate model in a range of systems. Even so, there are not many detailed studies available related to the stability analysis of fractional order systems with delay. In this work, we derive the stability conditions for linear fractional difference equations with an arbitrary delay τ and even for systems with distributed delay. We carry out a detailed stability analysis for the cases of single delay with τ=1 and τ=2. The results are extended to nonlinear maps. The formalism can be easily extended to multiple time delays.

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Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems

Cited by 4 publications

References 40 publications

Bidirectional coupling in fractional order maps of incommensurate orders

Bidirectional coupling in fractional order maps of incommensurate orders

Periodic Points, Stability, Bifurcations, and Transition to Chaos in Generalized Fractional Maps

Stability analysis of fractional difference equations with delay

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