Chaos in a nonlinear analog computer

We explore the chaotic behavior of a nonlinear electrical circuit constructed with simple components such as diodes and linear operational amplifiers. The circuit may be regarded as a nonlinear analog computer that gives a nearly exact solution of a particular chaotic model. Detailed comparisons between theoretical and experimental bifurcation points and power spectra yield differences of less than 1%. Keywords: Electronic chaos; nonlinear analog computer. The recent study of nonlinear dynamical systems has led to many intriguing and surprising results. One of these is the observation that certain systems can exhibit chaos, where small initial uncertainties grow exponentially in time giving large uncertainties in the future state of the system. Many examples of chaos have been found in nature and in numerical solutions of iterated maps and differential equations. However, the equations often poorly represent the phenomena they model and the agreement is usually at best qualitative. This paper reports a comparison between a simple model and an actual experiment with agreement that is better than 1% for such quantities as bifurcation points and power spectra. We consider a time-continuous system described by an autonomous ordinary differential equation (ODE) in a single variable, where the minimal conditions for chaos are that the ODE be thirdorder and contain a nonlinearity. Several authors have searched for the simplest third-order ODE that exhibits chao