Analysis and Synthesis of Realizable Non-equilibrium Dissipative Structures

Computation complexity of a broad variety of practical design problems is known to be strongly depending on an algebraic complexity of corresponding mathematical system representations. Especially some vector-matrix models are frequently used in numerous interdisciplinary fields. One way to overcome the complexity problems is based on some special algebraic structures of low order model approximations, such as e.g. balanced representations. Another approach based on the concept of sparse matrices has also become very popular. As a very successful special case of sparse matrix based approach a class of tridiagonal system representations [1] has found applications in solution of partial differential equations, digital signal processing, image processing, computational fluid dynamics, spline curve fitting and many others. In this contribution a generalized sparse matrix motivated multi-diagonal method is proposed and some new results, based on state space energy motivated causal system representations are presented, too [2]

A new chaotic system based on state space energy feedback

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems. A new four-scroll chaotic attractor was found by energy feedback controlling method in this paper. Spectral analysis shows that the system in the four-wing chaotic mode has very broad frequency bandwidth, verifying its random nature, and indicating the prospect for engineering applications such as secure communications, biology, etc. Creating a chaotic system with a more complicated topological structure such as a multi-scroll or multi-wing attractor, therefore, becomes a desirable task and sometimes a key issue for many engineering applications

Generalized tellegen principle used for energy method for systems modeling

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