This paper deals with dissipativity, stability, chaotic behavior and related structural properties of a relatively broad class of finite dimensional strictly causal systems. The class of nonlinear systems under consideration is described in the state-space representation form. System properties are investigated by a new approach based on a new abstract state energy concept, and on a proper generalization of the well known Tellegen's theorem as a form of the energy conservation principle. The resulting energy function is induced by the output signal power and determines both, the structure of a proper system representation as well as the corresponding system state space topology. The state minimality, as well as parameter minimality requirements plays a crucial role in the proposed method. Several examples are solved, and results of simulation are shown for illustration of fundamental ideas and basic attributes of the proposed method.