THREE-SCROLL UNIFIED CHAOTIC SYSTEM

Three-Scroll Unified Chaotic System (TSUCS) contains Lorenz-like subsystem and the Chen-like subsystem as two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz-like subsystem to the Chen-like subsystem and is chaotic over the entire spectrum of the key system parameter. The basic dynamical properties, such as Lyapunov exponents, fractal dimension, Poincare map and chaotic dynamical behaviors of the new unified chaotic system are studied, either numerically or analytically. Simulation results clearly show that this is a novel unified chaotic system and deserves further detailed investigation.

and a system of three ordinary differential equations describing the structure as-

$\left\{ \begin{eqnarray*} \frac{dx}{dt}&=&a(y-x)+d x z \\ \frac{dy}{dt}&=& bx-x z + f y \\ \frac{dz}{dt}&=& cz+xy-ex^2 \end{eqnarray*}\right. $

When a = 32.48, b = 45.84, c = 1.18, d = 0.13, e = 0.57 and f = 14.7, a solution curve of this system has the shape of wave like structure and the position of particles will follow a similar path.

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