Dynamics of nonlinear piecewise linearized circuit

This research addresses the analysis and control of a dynamic nonlinear system. An improved implementation of a nonlinear oscillator is proposed. The new realization combines attractive features of the current feedback op-amp (CFOA) operating in both voltage and current modes to construct the active three-segment voltage-controlled nonlinear resistor. The nonlinear resistor is evaluated in a piecewise linearized region for optimal stability. The control of the system is based on a linearized model the circuit, the useful tuning range of the major bifurcation parameter, and the expected frequency of oscillation can be estimated. The nonlinear system is broken into a piecewise linear system to investigate the differential equation and there challenging behavior in different regions of the piecewise linearize system. The closed form solution for the flow is given by three sets of equations representing the three solutions of the linear parts of system each valid in its respective domain defined by the boundaries of the piecewise linear function. The state transition from one domain to another occurs whenever the trajectory crosses one of the planes of the piecewise linear function. The equations are then used to form a nonlinear circuit realized with electrical components and plotted using an oscilloscope.