Stability and dynamics of complex order fractional difference equations

Sachin Bhalekar, Prashant M. Gade and Divya Joshi

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

Abstract: We extend the definition of n-dimensional difference equations to complex order. We investigate the stability of linear systems defined by an n-dimensional matrix and derive the conditions for the stability of zero solution of linear systems. For the one-dimensional case, we find that the stability region, if any is enclosed by a boundary curve and we obtain a parametric equation for the same. Furthermore, we find that there is no stable region if this parametric curve is self-intersecting. Even for the real eigenvalues, the solutions can be complex and dynamics in one-dimension is richer than the case for real order. These results can be extended to n-dimensions. For nonlinear systems, we observe that the stability of the linearized system determines the stability of the equilibrium point.

Keywords: Fractional difference equation; Complex order; Stability (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002739

DOI: 10.1016/j.chaos.2022.112063

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