On the Construction of Dissipative Polynomial Nambu Systems with Limit Cycles

In this chapter we study nonlinear Nambu systems with canonical dissipation in four dimensions in which prescribed limit cycles arise. For this purpose we discuss some possibilities to apply concepts from the geometry of four-dimensional Euclidean spaces in order to construct a desired intersection by a set of planes and surfaces. Since scalar Nambu functions are needed for the construction of Nambu systems, the relationship between these functions and hypersurfaces will be discussed. We illustrate our considerations by means of two examples of canonical dissipative (CD) Nambu systems in which limit cycles occur. Whereas we considered the synthesis problem of limit cycle circuits with the CD Nambu approach previously, we introduce in this paper an analysis concept based on CD Nambu systems for calculating nonisolated zeros of nonlinear equations.