On some extended Routh–Hurwitz conditions for fractional-order autonomous systems of order α ∈ (0, 2) and their applications to some population dynamic models

Abstract

Abstract The Routh–Hurwitz stability criterion is a useful tool for investigating the stability property of linear and nonlinear dynamical systems by analyzing the coefficients of the corresponding characteristic polynomial without calculating the eigenvalues of its Jacobian matrix. Recently some of these conditions have been generalized to fractional systems of order α ∈ [0, 1). In this paper we extend these results to fractional systems of order α ∈ [0, 2). Stability diagram and phase portraits classification in the (τ, Δ)-plane for planer fractional-order system are reported. Finally some numerical examples from population dynamics are employed to illustrate our theoretical results.