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Delay‐differential equations with discrete feedback: explicit formulae for infinitely many coexisting periodic solutions
Author(s) -
Bayer W.,
Heiden U.
Publication year - 2007
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200210329
Subject(s) - piecewise , delay differential equation , mathematics , nonlinear system , jump , constant (computer programming) , differential equation , differential (mechanical device) , mathematical analysis , negative feedback , control theory (sociology) , physics , computer science , control (management) , quantum mechanics , artificial intelligence , thermodynamics , programming language , voltage
It is well‐known that the combination of nonlinear feedback and temporal delay may create very complicated behavior, including infinitely many bifurcations and chaos. In this paper a differential delay equation is studied in case that the nonlinearity is piecewise constant (with a single jump). The existence of infinitely many periodic solutions with different minimal periods is proved and explicit formulae for these solutions are presented, at once for positive and for negative feedback.