A new 4-D dynamical system exhibiting chaos is introduced in this work. The proposed nonlinear plant with chaos has an unstable rest point and a line of rest points. Thus, the new nonlinear plant exhibits hidden attractors. A detailed dynamic analysis of the new nonlinear plant using bifurcation diagrams is described. Synchronization result of the new nonlinear plant with itself is achieved using Integral Sliding Mode Control (ISMC). Finally, a circuit model using MultiSim of the new 4-D nonlinear plant with chaos is carried out for practical use.

In the recent years, chaotic systems with uncountable equilibrium points such as chaotic systems with line equilibrium and curve equilibrium have been studied well in the literature. This reports a new 3-D chaotic system with an axe-shaped curve of equilibrium points. Dynamics of the chaotic system with the axe-shaped equilibrium has been studied by using phase plots, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Furthermore, an electronic circuit implementation of the new chaotic system with axe-shaped equilibrium has been designed to check its feasibility. As a control application, we report results for the synchronization of the new system possessing an axe-shaped curve of equilibrium points.

Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported.

In the paper an improved method of calculation of the inductance and capacitances in the ?1 circuit for Class A, AB, B, and C resonant power amplifiers is presented. This method is based on an assumption that the quality factor of the inductor is inite and the capacitors are lossless. The input parameters for calculations are the amplifier load resistance, the transistor load resistance, the quality factor of the inductor, the loaded quality factor of the designed circuit, and the operating frequency. The presented method allows reducing the required regulation range of ?1 circuits elements In built resonant amplifiers as compared to the traditional calculation methods assuming lossless capacitors and inductor. This advantage is important, in particular, for long- and medium-wave transistor power amplifiers, where capacitances in ?1 circuits are high comparing to typical trimming capacitors.

We study an elegant snap system with only one nonlinear term, which is a quadratic nonlinearity. The snap systemdisplays chaotic attractors,which are controlled easily by changing a system parameter. By using analysis, simulations and a real circuit, the dynamics of such a snap system has been investigated. We also investigate backstepping based adaptive control schemes for the new snap system with unknown parameters.

A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.