Abstract
In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order system with line equilibrium. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, through the Lyapunov exponent spectrum and bifurcation graph of the system under the change of the initial value, the influence of fractional order q on the system state can be observed. That is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it.
Highlights
Through the Lyapunov exponent spectrum and bifurcation graph of the system under the change of the initial value, the influence of fractional order q on the system state can be observed. at is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it
In the numerical calculation of fractional chaotic systems, namely, discretization of fractional chaotic systems, many scholars have made some achievements based on frequency-domain method (FDM) [10], Adomian decomposition method (ADM) [5,6,7, 9, 11], and Adams–Bashforth–Moulton (ABM) algorithm [12, 13]
We propose a new fractional-order chaotic system with line equilibrium
Summary
Routh–Hurwitz criterion, the equilibrium E3 is stable. Routh–Hurwitz criterion, we obtain that the equilibrium E3 is critical stable. E blue attractors are shown in chaotic states. Fix a 5, b 2, and c 34; initial values of state variables [x0, y0, z0] [1, 2, z0]; let the z(0) vary from − 15 to 15 with step size of 0.3 and y(0) vary from − 20 to 20 with step size of 0.4.
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