Bidirectional coupling in fractional order maps of incommensurate orders

We study the stability of bidirectionally coupled integer and fractional-order maps. The system is further generalized to the case where both the equations have fractional order difference operators. We derive stability conditions for the synchronized fixed point in both cases. We show that this for...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2024-09, Vol.186, p.115324, Article 115324
Main Authors: Bhalekar, Sachin, Gade, Prashant M., Joshi, Divya D.
Format: Article
Language:English
Subjects:
Bidirectional coupling
Fractional order maps
Incommensurate order
Stability analysis
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Summary:We study the stability of bidirectionally coupled integer and fractional-order maps. The system is further generalized to the case where both the equations have fractional order difference operators. We derive stability conditions for the synchronized fixed point in both cases. We show that this formalism can be extended to inhomogeneous systems of N coupled map where any map can be of arbitrary fractional order or integer order. We give a solution to a specific case of a system with periodic disorder where alternate maps are of integer and fractional order or different fractional orders. •We study the bidirectional coupling of fractional difference equations.•The orders of the difference operators are incommensurate-fractional.•Linear and nonlinear systems are considered.•The expressions for the stable region are provided.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2024.115324