Control Instrumentation Systems by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9789811394195
Publisher: Springer Singapore

Table 2 presents the eigenvalues of the system given in (1). It is specious from Table 2 that the new system has all the eigenvalues with stable nature. Thus, the new system may have hidden attractors.Table 2Equilibrium point and eigenvalues of system (1) with

Equilibrium point

Eigenvalues

3 Dynamical Analysis of System (1)

Dynamical behaviour of the considered new proposed system is shown in the present section using some of the numerical method.

The new system has hyperchaotic behaviour with . Finite-time LEs for these sets of parameters are Hyperchaotic attractors of the new system with are revealed in Fig. 1. Poincaré map across plane of the new system is presented in Fig. 2. The dynamical behaviour/characteristics of the new system is investigated by plotting the finite-time Lyapunov spectrum (LS). The finite-time LS is plotted by finding the Lyapunov exponents with the fixed initial conditions and observation time T = 20,000 time unit. The LEs are calculated by the method of Wolf et al. algorithm [51] in MATLAB simulation environment. The finite-time Lyapunov spectrum with varying e keeping other parameter fixed in Fig. 3. Presence of the two positive natures of the Lyapunov exponents in Fig. 3 indicates the existence of hyperchaotic behaviour in the new system.

Fig. 1Hyperchaotic attractors with for system (1)

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