Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback

被引:64
作者
Campbell, SA
Belair, J
Ohira, T
Milton, J
机构
[1] UNIV CHICAGO HOSP,DEPT NEUROL,CHICAGO,IL 60637
[2] UNIV CHICAGO HOSP,COMM NEUROBIOL,CHICAGO,IL 60637
[3] MCGILL UNIV,CTR NONLINEAR DYNAM PHYSIOL & MED,MONTREAL,PQ,CANADA
[4] UNIV WATERLOO,DEPT APPL MATH,WATERLOO,ON N2L 3G1,CANADA
[5] UNIV MONTREAL,CTR RECH MATH,MONTREAL,PQ H3C 3J7,CANADA
[6] UNIV MONTREAL,DEPT MATH & STAT,MONTREAL,PQ,CANADA
[7] SONY COMP SCI LAB INC,TOKYO,JAPAN
关键词
D O I
10.1063/1.166134
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems. (C) 1995 American Institute of Physics.
引用
收藏
页码:640 / 645
页数:6
相关论文
共 32 条
[1]   COMPLEX DYNAMICS IN METAL-CUTTING [J].
BERGER, BS ;
ROKNI, M ;
MINIS, I .
QUARTERLY OF APPLIED MATHEMATICS, 1993, 51 (04) :601-612
[2]   FEEDBACK AND DELAYS IN NEUROLOGICAL DISEASES - A MODELING STUDY USING DYNAMIC-SYSTEMS [J].
BEUTER, A ;
BELAIR, J ;
LABRIE, C ;
BELAIR, J .
BULLETIN OF MATHEMATICAL BIOLOGY, 1993, 55 (03) :525-541
[3]  
Beuter Anne, 1991, Chaos, V1, P279, DOI 10.1063/1.165841
[4]   STABILITY CRITERIA FOR SECOND-ORDER DYNAMICAL SYSTEMS WITH TIME LAG [J].
BHATT, SJ ;
HSU, CS .
JOURNAL OF APPLIED MECHANICS, 1966, 33 (01) :113-&
[5]   DYNAMICS OF DELAYED SYSTEMS UNDER FEEDBACK-CONTROL [J].
BOE, E ;
CHANG, HC .
CHEMICAL ENGINEERING SCIENCE, 1989, 44 (06) :1281-1294
[6]   TRANSITION TO CHAOS FROM A TWO-TORUS IN A DELAYED FEEDBACK SYSTEM [J].
Boe, Eugene ;
Chang, Hsueh-Chia .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1991, 1 (01) :67-81
[8]  
BOESE FG, 1994, CAN APPL MATH Q, V2, P151
[9]  
Campbell S. A., 1995, J DYN DIFFER EQU, V7, P213, DOI [10.1007/BF02218819, DOI 10.1007/BF02218819]
[10]  
CAMPBELL SA, IN PRESS CAN APPL MA