A cyclic system with delay and its characteristic equation
Elena Braverman, Karel Hasik, Anatoli F. Ivanov, Sergei Trofimchuk
TL;DR
This paper analyzes a nonlinear cyclic system with delay, deriving conditions for oscillation and monotone solutions based on the roots of its characteristic equation.
Contribution
It provides detailed analysis of the characteristic equation and establishes new sufficient conditions for oscillation and monotonicity in delayed cyclic systems.
Findings
Conditions for oscillation of solutions
Criteria for existence of monotone solutions
Detailed analysis of the characteristic equation
Abstract
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the existence of monotone solutions are derived in terms of roots of the characteristic equation.
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