Solution multistability in first-order nonlinear differential delay equations.

The dependence of solution behavior to perturbations of the initial function (IF) in a class of nonlinear differential delay equations (DDEs) is investigated. The structure of basins of attraction of multistable limit cycles is investigated. These basins can possess complex structure at all scales measurable numerically although this is not necessarily the case. Sensitive dependence of the asymptotic solution to perturbations in the initial function is also observed experimentally using a task specific electronic analog computer designed to investigate the dynamics of an integrable first-order DDE.

[1]  J. Dai,et al.  CHAOS IN LIQUID CRYSTAL OPTICAL BISTABILITY , 1988 .

[2]  André Longtin,et al.  Evaluation of pupil constriction and dilation from cycling measurements , 1990, Vision Research.

[3]  Raymond Kapral,et al.  Noisy Delay-Differential Equations In Optical Bistability , 1986, Other Conferences.

[4]  Michael C. Mackey,et al.  The dynamics of production and destruction: Analytic insight into complex behavior , 1982 .

[5]  André Longtin,et al.  Nonlinear oscillations, noise and chaos in neural delayed feedback , 1989 .

[6]  R. Vallée,et al.  Mode description of the dynamical evolution of an acousto-optic bistable device , 1985 .

[7]  D. Walls,et al.  Anomalous switching in dispersive optical bistability , 1979 .

[8]  Celso Grebogi,et al.  Fractal Basin Boundaries with Unique Dimension a , 1987 .

[9]  Hans-Otto Walther,et al.  Homoclinic solution and chaos in , 1981 .

[10]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[11]  J. Yorke,et al.  Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics , 1987, Science.

[12]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[13]  B. Hao,et al.  BIFURCATION SPECTRUM IN A DELAY-DIFFERENTIAL SYSTEM RELATED TO OPTICAL BISTABILITY , 1989 .

[14]  K. Ikeda,et al.  High-dimensional chaotic behavior in systems with time-delayed feedback , 1987 .

[15]  L. Glass,et al.  Delayed visual feedback and movement control in Parkinson's disease , 1990, Experimental Neurology.

[16]  Celso Grebogi,et al.  Structure and crises of fractal basin boundaries , 1985 .

[17]  J. M. Aguirregabiria,et al.  Fractal basin boundaries of a delay-differential equation , 1987 .

[18]  Longtin.  Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[19]  Longtin,et al.  Noise and critical behavior of the pupil light reflex at oscillation onset. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[20]  H. Gibbs,et al.  Observation of chaos in optical bistability (A) , 1981 .

[21]  Delay Equations, Approximation and Application , 1985 .

[22]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[23]  Delisle,et al.  Periodicity windows in a dynamical system with a delayed feedback. , 1986, Physical review. A, General physics.

[24]  B. Hao,et al.  Directions in chaos , 1987 .

[25]  K. Ikeda,et al.  Successive Higher-Harmonic Bifurcations in Systems with Delayed Feedback , 1982 .

[26]  Michael C. Mackey,et al.  Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors , 1989 .

[27]  Michael C. Mackey,et al.  Feedback, delays and the origin of blood cell dynamics , 1990 .

[28]  Dorizzi,et al.  Statistics and dimension of chaos in differential delay systems. , 1987, Physical review. A, General physics.

[29]  K. Ikeda.  Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system , 1979 .