Controlling the phase of an oscillator: A phase response curve approach

The paper discusses elementary control strategies to control the phase of an oscillator. Both feedforward and feedback (P and PI) control laws are designed based on the phase response curve (PRC) calculated from the linearized model. The performance is evaluated on a popular model of circadian oscillations.

[1]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[2]  Eric Shea-Brown,et al.  On the Phase Reduction and Response Dynamics of Neural Oscillator Populations , 2004, Neural Computation.

[3]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[4]  P. Tass.  Phase Resetting in Medicine and Biology , 1999 .

[5]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[6]  Francis J. Doyle,et al.  Circadian phase entrainment via nonlinear model predictive control , 2006 .

[7]  A. Winfree.  The geometry of biological time , 1991 .

[8]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[9]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[10]  Eduardo D. Sontag,et al.  Mathematical control theory: deterministic finite dimensional systems (2nd ed.) , 1998 .

[11]  P. Danzl,et al.  Spike timing control of oscillatory neuron models using impulsive and quasi-impulsive charge-balanced inputs , 2008, 2008 American Control Conference.

[12]  Alexander L. Fradkov,et al.  Introduction to Control of Oscillations and Chaos , 1998 .

[13]  Vladimir I. Babitsky,et al.  Dynamics and control of machines , 2000 .

[14]  J. Kurths,et al.  Automatic control of phase synchronization in coupled complex oscillators , 2005, Proceedings. 2005 International Conference Physics and Control, 2005..

[15]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[16]  Ilʹi︠a︡ Izrailevich Blekhman,et al.  Synchronization in science and technology , 1988 .

[17]  A. Goldbeter,et al.  Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora , 1999, Journal of biological rhythms.

[18]  A. S. Kovaleva.  Frequency and phase control of the resonance oscillations of a non-linear system under conditions of uncertainty† , 2004 .

[19]  Peter A. Tass,et al.  Phase Resetting in Medicine and Biology: Stochastic Modelling and Data Analysis , 1999 .

[20]  E. Mosekilde,et al.  Chaotic Synchronization: Applications to Living Systems , 2002 .

[21]  Germán Mato,et al.  Synchrony in Excitatory Neural Networks , 1995, Neural Computation.

[22]  Francis J. Doyle,et al.  Circadian Phase Resetting via Single and Multiple Control Targets , 2008, PLoS Comput. Biol..

[23]  D Gonze,et al.  Theoretical models for circadian rhythms in Neurospora and Drosophila. , 2000, Comptes rendus de l'Academie des sciences. Serie III, Sciences de la vie.

[24]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[25]  V. A. I︠A︡kubovich,et al.  Linear differential equations with periodic coefficients , 1975 .