Modified Chua’s Circuit in Different State Spaces

The paper deals with the development of theoretical backgrounds to design chaotic systems. These backgrounds are based on the use of coordinate transformations to represent system dynamics of known chaotic systems in various state spaces. The use of such an approach allows us to combine one state variable in different state spaces. In this case novel chaotic motions occur as result of changing inner system state variables. The main benefit of such an approach is a fact that if chaotic oscillations is generated in one state space then they occur in others too. This fact does not require to check Lyapunov exponents and other chaotic indicator for the transformed system. As a basis to perform coordinate transformation we consider defining series of Lie derivatives for the selected output state variable. Because of necessity to differentiate this variable one should consider chaotic system with differentiable nonlinearities. In case of the usage piecewise linear functions one should perform their smoothing by using various differentiable functions. The transformed chaotic system can be implemented in both continuous and discrete time domains by using various elements.