Bifurcation Analysis and Stability Criterion for the Nonlinear Fractional‐Order Three‐Dimensional Financial System with Delay

Abstract

In this paper, we study the dynamic characteristics of fractional-order nonlinear financial systems, including bifurcation and local asymptotic stability. Among them, we select the elasticity of demand of commercial (EDC) as the bifurcation point to discuss the state of the system. By calculating, the lowest order bifurcation point is obtained. Furthermore, the impulse control gains that follow a fractional-order control law are applied to make the fractional-order nonlinear financial system stable. In addition, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed state form of the system near the bifurcation point and the states of the system when the impulse control is used or not.

New results on finite‐time stability of fractional‐order Cohen–Grossberg neural networks with time delays

“…Numerous interesting works on asymp-totically stable, Mittag-Leffler stability, exponential stability, and uniform stability have been reported. However, all these contributions are concerned with the behavior of the systems over the infinite time interval [22][23][24]. In fact, finite-time stability (FTS) has attracted much interests of the scholars because in many practical applications, the primary concern is the behavior of the systems within the finite-time interval [25][26][27].…”

Adaptive fault‐tolerant control for fractional‐order fuzzy financial time‐delay system

“…And an estimated-fault-based investment policy is designed to regulate the addressed financial system. For this purposiveness, the following financial system [6] is given as,…”

“…0 and w ≠ 0(see [6]). And let ̄ir = i r − i * r , ̄id = i d − i * d and p = p − p * , then (1) can be rewritten as…”

“…As in meantime, fractional-order (FO) derivative representation gives more pliable approach for a practical system. Thus, taking the order of the system as fractional gives more flux for finance system [3][4][5][6][7]. In addition Senpagam et al [8] is a novel work which deals the financial system with independent order.…”

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

“…[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] More and more researchers are studying fractional systems and have gained results related to the fractional-order system. [32][33][34][35][36][37][38][39][40] In particular, in, [23] new results on the stabilization of fractional-order nonlinear systems, which lays a foundation for the research of fractional-order systems in the future is proposed. The other advantage is that fractional calculus theory is an excellent instrument to describe memory and the hereditary properties of processes [35] which can provide a wider stability region in the complex network and allow us to increase the scope of the study and enhance the accuracy.…”