Abstract
In this work, we announce a 3-D six-term novel chaotic system with a quartic nonlinearity. Next, the qualitative properties of the novel chaotic system are discussed in detail. We show that the novel chaotic system has three unstable equilibrium points. The Lyapunov exponents of the novel chaotic system are obtained as \(L_1 = 0.1507\), \(L_2 = 0\) and \(L_3 =-0.9521\), while the Kaplan–Yorke dimension of the novel chaotic system is obtained as \(D_{KY} = 2.1583\). The maximal Lyapunov exponent (MLE) of the novel chaotic system is obtained as \(L_1 = 0.1507\). Using Lyapunov stability theory, this work also derives an adaptive controller for the generalized projective synchronization (GPS) of identical novel chaotic systems with unknown parameters. In the chaos literature, many types of synchronization such as complete synchronization (CS), anti-synchronization (AS), hybrid synchronization (HS), projective synchronization (PS) and generalized synchronization (GS) are considered for the synchronization of a pair of chaotic systems called master and slave systems. All these types of synchronization are special cases of the generalized projective synchronization (GPS) of chaotic systems. MATLAB plots have been depicted to illustrate the phase portraits of the novel chaotic system and also the GPS results for the novel chaotic systems using adaptive controllers.
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