Chaos Control of a Fractional‐Order Financial System

Abstract

Fractional-order financial system introduced by W.-C. Chen (2008) displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreover numerical simulations are shown to verify the effectiveness of the proposed control scheme.

Bifurcations and chaos in a discrete SI epidemic model with fractional order

“…Over the years, numerous epidemiological models have been formulated mathematically (see, e.g., [1][2][3][4][5][6]). Although most of these models have been restricted to integer-order differential equations (IDEs), in the last three decades, it has turned out that many problems in different fields such as sciences, engineering, finance, economics and in particular epidemiology can be described successfully by the fractional-order differential equations (FDEs) (see, e.g., [7][8][9][10][11][12]). A property of these fractional-order models is their nonlocal property which does not exist in IDEs.…”

Fractional Order Model of Phytoplankton-toxic Phytoplankton-Zooplankton System

“…Indeed, we can find numerous applications in polymer rheology, regular variation in thermodynamics, aerodynamics, biophysics, blood flow phenomena, electrodynamics of complex medium, viscoelasticity, electroanalytical chemistry, biology, Bode analysis of feedback amplifiers, capacitor theory, electrical circuits, control theory, fitting of experimental data, etc. see for example [3,4,5], interest in fractional calculus and fractional differential equations has grown dramatically in recent decades [6,7]. The rest of this paper is organized as follows.…”

Parallel Simulations for Fractional-Order Systems

“…However, chaotic behavior has been observed by numerical simulations in many systems such as: a fractional-order Van der Pol system [1], fractional-order Chua and Chen's systems [2,3], a fractionalorder Rossler system [4] and a fractional-order financial system [5]. Nevertheless, it is worth noting that numerical simulations are limited by the fact that they only reveal the chaotic behavior of discrete-time dynamical systems that are obtained by discretizing the fractional-order systems.…”