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Abstract
In this paper, analytical results about the complex dynamics of a second-order digital filter with a zeroing-type characteristic are presented. A parametric plane is divided into subdomains where the dynamical system has the same qualitative behaviour. The structure of the attractor in each subdomain is described. In particular, the domain where the asymptotically unstable trivial fixed point is the global attractor is pointed out. The necessary conditions of the existence of non-trivial cycles are established. It is shown that non-trivial cycles exist only for a zero Lebesgue measure set of parameters. Results concerning non-periodic attractors and their structure are obtained. In particular, the domain where the attractor is formed by a set of half-intervals is determined.
Notes
†A shorter form of this paper was presented at the 1994 Workshop on the Nonlinear Dynamics of Electronic Systems (NDES'94) held at the University of Mining and Metallurgy. Krak[odot]w, Poland, on 29-30 July.