Stability of two-component incommensurate fractional-order systems and applications to the investigation of a FitzHugh-Nagumo neuronal model

Abstract

For two-dimensional autonomous linear incommensurate fractional-order dynamical systems with Caputo derivatives of different orders, necessary and sufficient conditions are obtained for the asymptotic stability and instability of the null solution. These conditions are expressed in terms of the elements of the system's matrix, as well as of the fractional orders of the Caputo derivatives, leading to a generalization of the well known Routh-Hurwitz conditions. These theoretical results are then used to investigate the stability properties of a two-dimensional fractional-order FitzHugh-Nagumo neuronal model. The occurrence of Hopf bifurcations is also discussed. Numerical simulations are provided with the aim of exemplifying the theoretical results, revealing rich spiking behavior, in comparison with the classical integer-order FitzHugh-Nagumo model.

13 pages, 4 figures. arXiv admin note: text overlap with arXiv:1612.05389

References in corpus (3)

• A Novel Exact Representation of Stationary Colored Gaussian Processes (Fractional Differential Approach)
• Stability properties of a two-dimensional system involving one Caputo derivative and applications to the investigation of a fractional-order Morris-Lecar neuronal model
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Cited by in corpus (4)

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• Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems
• Stability Properties of Multi-Order Fractional Differential Systems in 3D