Chaotic Dynamics, Chaos Synchronization, State Estimation, and Interpretation Using Electrical Elements and Circuits

Chaotic systems and chaotic signal synchronization have attracted a lot of attention lately. Most work on chaotic systems is based on few well-known 3rd-order models derived using analytical techniques. In addition, chaotic signal synchronization or the inability to achieve the same is proven using analytical concepts such as Lyapunov constants etc. that could be understood only by those mathematically gifted. Such methods also have limitations such as the initial state of the coupled chaotic systems cannot be too far away etc. Most of these problems are associated with the application of complex analytical techniques to an area which itself is too complex, forcing us to settle for special models, assumptions, etc. In this paper, we consider two major problems, 1) Design of Chaotic Systems, and 2) Chaos synchronization, from an electrical circuits’ perspective, and show how an elegant solution to these two problems can be achieved from a new approach that we call as the building block approach. This approach minimizes the need for complex analytical techniques (or moves the complexity away from a macro or global level to a micro or local level) in analyzing and or designing such systems, and more importantly, gives us the ability to concentrate more on what we can achieve from such complex systems. We will also cast the problem of chaotic signal synchronization in the form of state estimation given partial state observation (except that here we are dealing with a transmitter that is a complex quasi-stable system) and hence the solution that we propose here applies to the general problem of state estimation as well.