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Bidirectional coupling in fractional order maps of incommensurate orders

Author

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  • Bhalekar, Sachin
  • Gade, Prashant M.
  • Joshi, Divya D.

Abstract

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.

Suggested Citation

  • Bhalekar, Sachin & Gade, Prashant M. & Joshi, Divya D., 2024. "Bidirectional coupling in fractional order maps of incommensurate orders," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008762
    DOI: 10.1016/j.chaos.2024.115324
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    References listed on IDEAS

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    1. Bhalekar, Sachin & Gade, Prashant M. & Joshi, Divya, 2022. "Stability and dynamics of complex order fractional difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Pakhare, Sumit S. & Bhalekar, Sachin & Gade, Prashant M., 2022. "Synchronization in coupled integer and fractional-order maps," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Mashayekhi, S. & Sedaghat, S., 2021. "Fractional model of stem cell population dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Joshi, Divya D. & Bhalekar, Sachin & Gade, Prashant M., 2023. "Controlling fractional difference equations using feedback," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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