Nonlinear dynamics, adaptative control and synchronization of a finance system with integer and fractional order

E.I.S. Akpado, C.H. Miwadinou, C. Ainamon, A.V. Monwanou and J.B. Chabi Orou

Chaos, Solitons & Fractals, 2026, vol. 202, issue P1

Abstract: This work studies the complex dynamics, adaptive control and synchronization of a novel finance system. This system is a generalization of the finance system proposed by Johansyash et al. and incorporates fractional derivatives. After determining the fixed points of the novel finance system with fractional order, the study of their stability allowed finding the values of the order of the fractional derivative for which the fixed points are stable. Using Adam Bashford Moulton’s Predictor-Corrector method, the bifurcation diagram and the Lyapunov exponent are determined numerically in the commensurable and non-commensurable case. Adaptive control and chaotic synchronization are done by the adaptive method and using the Lyapunov function in the case of integer-order derivative and in the commensurable case of fractional derivative. Numerical simulations confirmed and supplemented the analytical results.

Keywords: Nonlinear dynamics; a novel finance system; Fractional order; Synchronization; Adaptative control (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:202:y:2026:i:p1:s0960077925015747

DOI: 10.1016/j.chaos.2025.117561

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