On the conditions for cycles existence in a second-order discrete-time system with sector-nonlinearity

In this paper, a second-order discrete-time automatic control system is studied. This work continuation of the research presented in author’s papers “On Aizerman problem: coefficient conditions for existence four-period cycle system” and threeand six-period cycles system”, where systems with two- three-periodic nonlinearities lying Hurwitz angle were considered. The subjected to stronger constraints are discussed paper. It assumed that nonlinearity not only lies angle, but also satisfies additional sector-condition. formulation problem found many works devoted theoretical applied questions theory. such explored all possible values parameters. shown case there parameter which two-periodic has family cycles, three- or cycles. on parameters under can have periodic solutions written out explicitly. proofs theorems provide method constructing way any solution initial data some definite ray periodic.