Circuit design and implementation of Lorenz chaotic system with one parameter

Abstract

To study the characteristics of the chaotic systems and their applications, an electronic circuit of simplified Lorenz chaotic system with one parameter is designed and experimented with discrete components. The system parameters correspond to the circuit element parameters. By regulating the variable resistor in the circuit, dynamic behaviors including limit cycle, pitchfork bifurcation, period-doubling bifurcation, chaos, and route to chaos by period-doubling bifurcation, are observed. The necessary condition for the existence of chaos in the fractional-order simplified Lorenz system is deduced. The lowest order of the fractional-order simplified Lorenz system and the variation law of the lowest order with system parameters are determined. Circuit simulations and experiments show that the simplified Lorenz system has rich dynamic characteristics, and that theoretical analysis and circuit experiment are accordant with each other.