Stability and dynamics of complex order fractional difference equations

Gade, Prashant M.; Joshi, Divya

doi:10.1016/j.chaos.2022.112063

Cited by 11 publications

(1 citation statement)

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“…Semi-analytic and numerical results for the case of fractional (power-law kernel) standard and logistic maps were obtained in [20,21] (see also reviews [4,22]). Later, the problem of the linear asymptotic stability was considered for the case of fractional difference equations (falling factorial kernel) [23][24][25] and, recently, for the case of the complex order fractional difference equations [26]. In the general case of the discrete convolution equations, the conditions of stability were formulated as the requirements on zeros of a characteristic equation.…”

Section: Introductionmentioning

confidence: 99%

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1

Edelman

2022

Preprint

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Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convolutions with some power-law-like functions. The conditions of the asymptotic stability of the fixed points for maps of the orders 0 < α < 1 that are derived in this paper are narrower than the conditions of stability for the discrete convolution equations in general and wider than the well-known conditions of stability for the fractional difference maps. The derived stability conditions for the fractional standard and logistic maps coincide with the results previously observed in numerical simulations. In nonlinear maps, one of the derived limits of the fixed-point stability coincides with the fixed-point - asymptotically period two bifurcation point. PACS 05.45.Pq · 45.10.Hj Mathematics Subject Classification (2000) 47H99 60G99 · 34A99 · 39A70

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Section: Introductionmentioning

confidence: 99%

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1

Edelman

2022

Preprint

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

Bhalekar,

Gade

2023

J Nonlinear Sci

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Stability of fixed points in generalized fractional maps of the orders $$0< \alpha <1$$

Edelman

2023

Nonlinear Dyn

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Stability and dynamics of complex order fractional difference equations

Cited by 11 publications

References 23 publications

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1

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

Stability of fixed points in generalized fractional maps of the orders $$0< \alpha <1$$

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Stability and dynamics of complex order fractional difference equations

Cited by 11 publications

References 23 publications

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 &lt; α &lt; 1

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 &lt; α &lt; 1

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

Stability of fixed points in generalized fractional maps of the orders $$0< \alpha <1$$

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Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1

Stability of Fixed Points in Generalized Fractional Maps of the Orders 0 < α < 1