Oscillatory modes in a nonlinear second-order differential equation with delay

Autor:	André Longtin, John Milton, R. Scholl, U. an der Heiden, Michael C. Mackey
Rok vydání:	1990
Předmět:	Liénard equation Linear differential equation Homogeneous differential equation Differential equation Ordinary differential equation Mathematical analysis First-order partial differential equation Delay differential equation Universal differential equation Analysis Mathematics
Zdroj:	Journal of Dynamics and Differential Equations. 2:423-449
ISSN:	1572-9222 1040-7294
DOI:	10.1007/bf01054042
Popis:	Solution properties of the nonlinear second-order delay-differential equation x(t)=−ax(t)+f[x(t−Τ)] are studied wheref is a piecewise constant function which mimics negative feedback. We show that the solutions can be obtained by a simple geometrical construction which, in principle, can be implemented using a ruler and a compass. Analytical results guarantee the existence and stability properties of limit cycle solutions. Computer-aided constructions reveal a remarkable richness of different types of dynamical behaviors including a variety of unconventional bifurcation schemes.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c5fda3f892a7ebf44ec047b18b9515ee https://doi.org/10.1007/bf01054042 Zobrazit plný text záznamu Full text from SpringerLink