Eatures [22]. Some noticeable features will be the absence of linear terms, look of many equilibrium points, and multistability. Most research BI-0115 Inhibitor inside the field of chaotic systems have been focused on systems with linear terms. Having said that, final results primarily based upon systems without having linear terms are limited. Xu and Wang have been mentioned that there was a lot significantly less information about chaotic attractors devoid of a linear term [23]. Consequently, the authors constructed a program with natural logarithmic, exponential and quadratic terms. Employing six quadratic terms, a technique with eight equilibrium points was proposed in [24]. Zhang et al.Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in Hydroxyflutamide site published maps and institutional affiliations.Copyright: 2021 by the authors. Licensee MDPI, Basel, Switzerland. This short article is an open access report distributed under the terms and situations of the Creative Commons Attribution (CC BY) license (https:// 4.0/).Symmetry 2021, 13, 2142. 2021, 13,2 ofapplied a fractional derivative to get a brand new system with six quadratic terms [25]. The authors found four equilibrium points and twin symmetric attractors in Zhang’s technique. Previously published research on nonlinear systems paid specific interest to saddle point equilibrium in [26]. The existence of saddle point equilibrium is important to the style of chaotic systems [27]. Comparatively recent investigation has been located, concerned with distinctive equilibia [28,29]. Not too long ago, investigators have examined chaos in systems with infinite equilibrium [30,31]. A further particular function observed in nonlinear systems is multistability [32]. According to the initial conditions, coexisting attractors is often observed. Multistability has emerged as a powerful strategy for investigating asymmetric and symmetric attractors [335]. Interestingly, various attractors attract new analysis on memristor circuits [36,37]. In this paper, we study a oscillator with nonlinear terms (quadratic and cubic ones). In contrast with traditional systems, you’ll find infinite equilibria in our oscillator. The functions and dynamics of your oscillator are presented in Section two. Section 3 discusses the oscillator’s implementation. A mixture synchronization with the oscillator is reported in Section 4, whilst conclusions are offered inside the final section. two. Attributes and Dynamics in the Oscillator We take into account an oscillator described by x = yz y = x 3 – y3 z = ax2 by2 – cxy with parameters a, b, c 0. By solving the following equations: yz = 0 x three – y3 = 0 ax2 by2 – cxy = 0 we get the equilibrium points of oscillator (1): E (0, 0, z ) (3)(1)(two)Hence, oscillator (1) has an equilibrium line. Oscillator (1) is invariant under the transformation ( x, y, z) (- x, -y, z) (four) and oscillator (1) is symmetric. Note that the Jacobian matrix at E is 0 = 0 0 z 0 0 0 0JE(five)Thus, the characteristic equation is 3 = 0 and the eigenvalue = 0. We repair a = 0.2, b = 0.1 as well as the initial circumstances (0.1, 0.1, 0.1) although c is varied. The Lypunov exponents (Figure 1a) and bifurcation diagram (Figure 1b) for c are presented. As observed from Figure 1, the oscillator can create periodical signals and chaotic signals. For c = 0.5, chaotic attractors are displayed in Figure 2. We employed the Runge utta strategy for simulations and the Wolf’s algorithm for Lypunov exponent calculations [38]. Interestingly, the oscilla.