Energy-like functions for some dissipative chaotic systems

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lu-Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the R,Rossler system at least a fourth-order polynomial is required to properly represent its energy.