Making a dynamical system chaotic: feedback control of Lyapunov exponents for discrete-time dynamical systems

A simple, yet mathematically precise and rigorous, feedback control design procedure is suggested in this paper, which can rearrange all the Lyapunov exponents of the controlled system according to the user's desire, namely, to make them positive, zero, and/or negative in any desired order, for any given n-dimensional discrete-time smooth nonlinear dynamical system that could be originally nonchaotic or even asymptotically stable. The argument used is purely algebraic and the design procedure is completely schematic, without using any approximations throughout the derivation. A numerical example is included to visualize the anticontrol.