-
2
-
-
27144554216
-
Feedback for physicists: A tutorial essay on control
-
Bechhoefer, J., Feedback for physicists: A tutorial essay on control, Rev. Mod. Phys. 77, 2005, 783-836.
-
(2005)
Rev. Mod. Phys.
, vol.77
, pp. 783-836
-
-
Bechhoefer, J.1
-
3
-
-
0008867387
-
-
Oxford University Press, New York, NY
-
Bellen, A. and Zennaro, M., Numerical Methods for Delay Differential Equations, Oxford University Press, New York, NY, 2003.
-
(2003)
Numerical Methods for Delay Differential Equations
-
-
Bellen, A.1
Zennaro, M.2
-
4
-
-
0003759192
-
-
Wiley, New York, NY
-
Bendat, J. S. and Piersol, A. G., Random Data: Analysis and Measurement Procedures, 2nd Edition, Wiley, New York, NY, 1986.
-
(1986)
Random Data: Analysis and Measurement Procedures, 2nd Edition
-
-
Bendat, J.S.1
Piersol, A.G.2
-
5
-
-
0004232671
-
-
Princeton University Press, Princeton, NJ
-
Berg, H. C., Random Walks in Biology, Expanded Edition, Princeton University Press, Princeton, NJ, 1993.
-
(1993)
Random Walks in Biology, Expanded Edition
-
-
Berg, H.C.1
-
6
-
-
0004044016
-
-
Birkhäuser, Boston, MA
-
Boukas, E-K. and Liu Z-K., Deterministic and Stochastic Time Delay Systems, Birkhäuser, Boston, MA, 2002.
-
(2002)
Deterministic and Stochastic Time Delay Systems
-
-
Boukas, E.-K.1
Liu, Z.-K.2
-
7
-
-
0003488984
-
-
McGraw-Hill, New York, NY
-
Bracewell, R. N., The Fourier Transform and its Applications, 2nd Edition, McGraw-Hill, New York, NY, 1986.
-
(1986)
The Fourier Transform and Its Applications, 2nd Edition
-
-
Bracewell, R.N.1
-
8
-
-
26844581913
-
Delay-induced stochastic oscillations in gene regulation
-
Bratsun, D., Volfson, D., Tsimring, L. S. and Hasty, J., Delay-induced stochastic oscillations in gene regulation, Proc. Natl Acad. Sci. USA 102, 2005, 14593-14598.
-
(2005)
Proc. Natl Acad. Sci. USA
, vol.102
, pp. 14593-14598
-
-
Bratsun, D.1
Volfson, D.2
Tsimring, L.S.3
Hasty, J.4
-
9
-
-
4344708566
-
On-off intermittency in a human balancing task
-
Cabrera, J. L. and Milton, J. G., On-off intermittency in a human balancing task, Phys. Lett. Rev. 89, 2002, 158702.
-
(2002)
Phys. Lett. Rev.
, vol.89
, pp. 158702
-
-
Cabrera, J.L.1
Milton, J.G.2
-
10
-
-
7244257454
-
Human stick balancing: Tuning Lévy flights to improve balance control
-
Cabrera, J. L. and Milton, J. G., Human stick balancing: Tuning Lévy flights to improve balance control, Chaos 14, 2004, 691-698.
-
(2004)
Chaos
, vol.14
, pp. 691-698
-
-
Cabrera, J.L.1
Milton, J.G.2
-
11
-
-
7444256234
-
State-dependent noise and human balance control
-
Cabrera, J. L., Bormann, R., Eurich, C. W., Ohira, T. and Milton, J., State-dependent noise and human balance control, Fluct. Noise Lett. 4, 2004, L107-L117.
-
(2004)
Fluct. Noise Lett.
, vol.4
-
-
Cabrera, J.L.1
Bormann, R.2
Eurich, C.W.3
Ohira, T.4
Milton, J.5
-
12
-
-
33745946505
-
Neural control on multiple time scales: Insights from human stick balancing
-
Cabrera, J. L., Luciani, C., and Milton, J., Neural control on multiple time scales: Insights from human stick balancing, Condens. Matter Phys. 2, 2006, 373-383.
-
(2006)
Condens. Matter Phys.
, vol.2
, pp. 373-383
-
-
Cabrera, J.L.1
Luciani, C.2
Milton, J.3
-
13
-
-
0001178448
-
Random walking during quiet standing
-
Collins, J. J. and De Luca, C. J., Random walking during quiet standing, Phys. Rev. Lett. 73, 1994, 907-912.
-
(1994)
Phys. Rev. Lett.
, vol.73
, pp. 907-912
-
-
Collins, J.J.1
De Luca, C.J.2
-
14
-
-
85051993518
-
-
IEEE, New York, NY
-
Davenport, W. B. and Root, W. L., An Introduction to the Theory of Random Signals and Noise, IEEE, New York, NY, 1987.
-
(1987)
An Introduction to the Theory of Random Signals and Noise
-
-
Davenport, W.B.1
Root, W.L.2
-
15
-
-
0001123562
-
Über zwei bekannte Einwände gegan das Boltzmannsche H-Theorem
-
Ehrenfest, P. and Ehrenfest, T., Über zwei bekannte Einwände gegan das Boltzmannsche H-Theorem, Phys. Zeit. 8, 1907, 311-314.
-
(1907)
Phys. Zeit.
, vol.8
, pp. 311-314
-
-
Ehrenfest, P.1
Ehrenfest, T.2
-
16
-
-
84976701037
-
Zür Theorie der Brownschen Bewegung
-
Einstein, A., Zür Theorie der Brownschen Bewegung, Annalen der Physik 19, 1905, 371-381.
-
(1905)
Annalen der Physik
, vol.19
, pp. 371-381
-
-
Einstein, A.1
-
17
-
-
0001723273
-
Noise-induced transitions in human postural sway
-
Eurich, C.W. and Milton, J. G., Noise-induced transitions in human postural sway, Phys. Rev. E 54, 1996, 6681-6684.
-
(1996)
Phys. Rev. e
, vol.54
, pp. 6681-6684
-
-
Eurich, C.W.1
Milton, J.G.2
-
18
-
-
42749099704
-
Multidelayed random walk: Theory and application to the neolithic transition in Europe
-
Fort, J., Jana, D. and Humet, J., Multidelayed random walk: Theory and application to the neolithic transition in Europe, Phys. Rev. E. 70, 2004, 031913.
-
(2004)
Phys. Rev. E.
, vol.70
, pp. 031913
-
-
Fort, J.1
Jana, D.2
Humet, J.3
-
19
-
-
27244434621
-
Delay Fokker-Planck equations, Novikov's theorem, and Boltzmann distributions as small delay approximations
-
Frank, T. D., Delay Fokker-Planck equations, Novikov's theorem, and Boltzmann distributions as small delay approximations, Phys. Rev. E 72, 2005, 011112.
-
(2005)
Phys. Rev. e
, vol.72
, pp. 011112
-
-
Frank, T.D.1
-
20
-
-
0035420558
-
Stationary solutions of linear stochastic delay differential equations: Applications to biological systems
-
Frank, T. D. and Beek, P. J., Stationary solutions of linear stochastic delay differential equations: Applications to biological systems, Phys. Rev. E 64, 2001, 021917.
-
(2001)
Phys. Rev. e
, vol.64
, pp. 021917
-
-
Frank, T.D.1
Beek, P.J.2
-
21
-
-
0003392158
-
-
Springer, New York, NY
-
Gardiner, C. W., Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, Springer, New York, NY, 1994.
-
(1994)
Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
-
-
Gardiner, C.W.1
-
22
-
-
0003707162
-
-
Princeton University Press, Princeton, NJ
-
Glass, L. and Mackey, M. C., From Clocks to Chaos: The Rhythms of Life, Princeton University Press, Princeton, NJ, 1988.
-
(1988)
From Clocks to Chaos: The Rhythms of Life
-
-
Glass, L.1
Mackey, M.C.2
-
23
-
-
0001844761
-
Delay, feedback and quenching in financial markets
-
Grassia, P. S., Delay, feedback and quenching in financial markets, Eur. Phys. J. B 17, 2000, 347-362.
-
(2000)
Eur. Phys. J. B
, vol.17
, pp. 347-362
-
-
Grassia, P.S.1
-
24
-
-
0029255636
-
A robust hybrid stabilization strategy for equilibria
-
Guckhenheimer, J., A robust hybrid stabilization strategy for equilibria, IEEE Trans. Autom. Control 40, 1995, 321-326.
-
(1995)
IEEE Trans. Autom. Control
, vol.40
, pp. 321-326
-
-
Guckhenheimer, J.1
-
25
-
-
0000680355
-
Small delay approximation of stochastic delay differential equation
-
Guillouzic, S., L'Heureux, I. and Longtin, A., Small delay approximation of stochastic delay differential equation, Phys. Rev. E 59, 1999, 3970-3982.
-
(1999)
Phys. Rev. e
, vol.59
, pp. 3970-3982
-
-
Guillouzic, S.1
L'Heureux, I.2
Longtin, A.3
-
26
-
-
0003421845
-
-
Springer, New York, NY
-
Hale, J. and Koçak, H., Dynamics and Bifurcations, Springer, New York, NY, 1991.
-
(1991)
Dynamics and Bifurcations
-
-
Hale, J.1
Koçak, H.2
-
27
-
-
33746789080
-
A modified Milstein scheme for approximation of stochastic delay differential equation with constant time lag
-
Hofmann, N. and Müller-Gronbach, T., A modified Milstein scheme for approximation of stochastic delay differential equation with constant time lag, J. Comput. Appl. Math. 197, 2006, 89-121.
-
(2006)
J. Comput. Appl. Math.
, vol.197
, pp. 89-121
-
-
Hofmann, N.1
Müller-Gronbach, T.2
-
28
-
-
33745278574
-
Balancing with noise and delay
-
Hosaka, T., Ohira, T., Luciani, C., Cabrera, J. L. and Milton, J. G., Balancing with noise and delay, Prog. Theor. Phys. Suppl. 161, 2006, 314-319.
-
(2006)
Prog. Theor. Phys. Suppl.
, vol.161
, pp. 314-319
-
-
Hosaka, T.1
Ohira, T.2
Luciani, C.3
Cabrera, J.L.4
Milton, J.G.5
-
29
-
-
2142818234
-
Discrete time approximations of stochastic delay equations: The Milstein scheme
-
Hu, Y., Mohammed, S.-E. A. and Yan, F., Discrete time approximations of stochastic delay equations: the Milstein scheme, Ann. Probab. 32, 2004, 265-314.
-
(2004)
Ann. Probab.
, vol.32
, pp. 265-314
-
-
Hu, Y.1
Mohammed, S.-E.A.2
Yan, F.3
-
30
-
-
0003803467
-
-
Holden-Day, San Francisco, CA
-
Jenkins, G. M. and Watts, D. G., Spectral Analysis and its Applications, Holden-Day, San Francisco, CA, 1968.
-
(1968)
Spectral Analysis and Its Applications
-
-
Jenkins, G.M.1
Watts, D.G.2
-
31
-
-
0001755583
-
Random walk and the theory of Brownian motion
-
Kac, M., Random walk and the theory of Brownian motion, Am. Math. Monthly 54, 1947, 369-391.
-
(1947)
Am. Math. Monthly
, vol.54
, pp. 369-391
-
-
Kac, M.1
-
32
-
-
0040867061
-
Ehrenfest urn models
-
Karlin, S. and McGregor, J., Ehrenfest urn models, J. Appl. Prob. 2, 1965, 352-376.
-
(1965)
J. Appl. Prob.
, vol.2
, pp. 352-376
-
-
Karlin, S.1
McGregor, J.2
-
33
-
-
0001840597
-
Langevins stochastic differential equation extended by a timedelayed term
-
Küchler, U. and Mensch, B., Langevins stochastic differential equation extended by a timedelayed term, Stoch. Stoch. Rep. 40, 1992, 23-42.
-
(1992)
Stoch. Stoch. Rep.
, vol.40
, pp. 23-42
-
-
Küchler, U.1
Mensch, B.2
-
34
-
-
22144492804
-
Dynamics of an inverted pendulum with delayed feedback control
-
Landry, M., Campbell, S. A., Morris, K. and Aguilar, C. O., Dynamics of an inverted pendulum with delayed feedback control, SIAM J. Dynam. Syst. 4, 2005, 333-351.
-
(2005)
SIAM J. Dynam. Syst.
, vol.4
, pp. 333-351
-
-
Landry, M.1
Campbell, S.A.2
Morris, K.3
Aguilar, C.O.4
-
35
-
-
0004116528
-
-
Springer, New York, NY
-
Lasota, A. and Mackey, M. C., Chaos, Fractals and Noise: Stochastic Aspects of Dynamics, Springer, New York, NY, 1994.
-
(1994)
Chaos, Fractals and Noise: Stochastic Aspects of Dynamics
-
-
Lasota, A.1
Mackey, M.C.2
-
36
-
-
0000069284
-
Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation
-
Longtin, A., Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation, Phys. Rev. A 44, 1991, 4801-4813.
-
(1991)
Phys. Rev. A
, vol.44
, pp. 4801-4813
-
-
Longtin, A.1
-
37
-
-
0001087201
-
Noise and critical behavior of the pupil light reflex at oscillation onset
-
Longtin, A., Milton, J. G., Bos, J. E., and Mackey, M. C., Noise and critical behavior of the pupil light reflex at oscillation onset, Phys. Rev. A 41, 1990, 6992-7005.
-
(1990)
Phys. Rev. A
, vol.41
, pp. 6992-7005
-
-
Longtin, A.1
Milton, J.G.2
Bos, J.E.3
Mackey, M.C.4
-
38
-
-
0036588349
-
Human balancing of an inverted pendulum: Position control by small, ballistic-like, throw and catch movements
-
Loram, I. D. and Lakie, M., Human balancing of an inverted pendulum: position control by small, ballistic-like, throw and catch movements, J. Physiol. 540, 2002, 1111-1124.
-
(2002)
J. Physiol.
, vol.540
, pp. 1111-1124
-
-
Loram, I.D.1
Lakie, M.2
-
39
-
-
17444412715
-
Active, non-spring-like muscle movements in human postural sway: How might paradoxical changes in muscle length be produced?
-
Loram, I. D., Maganaris, C. N. and Lakie, M., Active, non-spring-like muscle movements in human postural sway: how might paradoxical changes in muscle length be produced? J. Physiol. 564.1, 2005, 281-293.
-
(2005)
J. Physiol.
, vol.564
, Issue.1
, pp. 281-293
-
-
Loram, I.D.1
Maganaris, C.N.2
Lakie, M.3
-
42
-
-
5544290000
-
Noise and stability in differential delay equations
-
Mackey, M. C. and Nechaeva, I. G., Noise and stability in differential delay equations, J. Dynam. Diff. Eqns. 6, 1994, 395-426.
-
(1994)
J. Dynam. Diff. Eqns.
, vol.6
, pp. 395-426
-
-
Mackey, M.C.1
Nechaeva, I.G.2
-
43
-
-
5544262166
-
Solution moment stability in stochastic differential delay equations
-
Mackey, M. C. and Nechaeva, I. G., Solution moment stability in stochastic differential delay equations, Phys. Rev. E 52, 1995, 3366-3376.
-
(1995)
Phys. Rev. e
, vol.52
, pp. 3366-3376
-
-
Mackey, M.C.1
Nechaeva, I.G.2
-
46
-
-
34047189124
-
Modeling the control of fixational eye movements with neurophysiological delays
-
Mergenthaler, K. and Enghert, R., Modeling the control of fixational eye movements with neurophysiological delays, Phys. Rev. Lett. 98, 2007, 138104.
-
(2007)
Phys. Rev. Lett.
, vol.98
, pp. 138104
-
-
Mergenthaler, K.1
Enghert, R.2
-
47
-
-
34548122290
-
Oscillations and multistability in delayed feedback control
-
(H. G. Othmer, F. R. Adler, M. A. Lewis and J. C. Dallon (eds). Prentice Hall, Upper Saddle River, NJ
-
Milton, J. and Foss, J., Oscillations and multistability in delayed feedback control. In:Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology (H. G. Othmer, F. R. Adler, M. A. Lewis and J. C. Dallon (eds). Prentice Hall, Upper Saddle River, NJ, pp. 179-198, 1997.
-
(1997)
Case Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology
, pp. 179-198
-
-
Milton, J.1
Foss, J.2
-
48
-
-
0024976331
-
Complex dynamics and bifurcations in neurology
-
Milton, J. G., Longtin, A., Beuter, A., Mackey, M. C. and Glass, L., Complex dynamics and bifurcations in neurology, J. Theor. Biol. 138, 1989, 129-147.
-
(1989)
J. Theor. Biol.
, vol.138
, pp. 129-147
-
-
Milton, J.G.1
Longtin, A.2
Beuter, A.3
Mackey, M.C.4
Glass, L.5
-
49
-
-
79051469306
-
Unstable dynamical systems: Delays, noise and control
-
Milton, J. G., Cabrera, J. L. and Ohira, T., Unstable dynamical systems: Delays, noise and control, Europhys. Lett. 83, 2008, 48001.
-
(2008)
Europhys. Lett.
, vol.83
, pp. 48001
-
-
Milton, J.G.1
Cabrera, J.L.2
Ohira, T.3
-
50
-
-
84892281445
-
Balancing with positive feedback: The case for discontinuous control
-
(submitted)
-
Milton, J., Townsend, J. L., King, M. A. and Ohita, T., Balancing with positive feedback: The case for discontinuous control, Philos. Trans. R. Soc. (submitted).
-
Philos. Trans. R. Soc.
-
-
Milton, J.1
Townsend, J.L.2
King, M.A.3
Ohita, T.4
-
52
-
-
0031484968
-
Lyapunov exponents of linear stochastic functional differential equations. Part II. Examples and case studies
-
Mohammed, S.-E. A. and Scheutzow, M. K. R., Lyapunov exponents of linear stochastic functional differential equations. Part II. Examples and case studies, Ann. Probab. 25, 1997, 1210-1240.
-
(1997)
Ann. Probab.
, vol.25
, pp. 1210-1240
-
-
Mohammed, S.-E.A.1
Scheutzow, M.K.R.2
-
53
-
-
0031023949
-
Stochastic processes in postural center-of-pressure profiles
-
Newell, K. M., Slobounov, S. M., Slobounova, E. S. and Molenaar, P. C. M., Stochastic processes in postural center-of-pressure profiles, Exp. Brain Res. 113, 1997, 158-164.
-
(1997)
Exp. Brain Res.
, vol.113
, pp. 158-164
-
-
Newell, K.M.1
Slobounov, S.M.2
Slobounova, E.S.3
Molenaar, P.C.M.4
-
54
-
-
11144345488
-
-
Springer, New York, NY
-
Niculescu, S.-I. and Gu, K., Advances in Time-Delay Systems, Springer, New York, NY, 2004.
-
(2004)
Advances in Time-Delay Systems
-
-
Niculescu, S.-I.1
Gu, K.2
-
55
-
-
0000157099
-
Oscillatory correlation of delayed random walks
-
Ohira, T., Oscillatory correlation of delayed random walks, Phys. Rev. E 55, 1997, R1255-R1258.
-
(1997)
Phys. Rev. e
, vol.55
-
-
Ohira, T.1
-
56
-
-
33244489249
-
Delayed random walks
-
Ohira, T. and Milton, J., Delayed random walks, Phys. Rev. E 52, 1995, 3277-3280.
-
(1995)
Phys. Rev. e
, vol.52
, pp. 3277-3280
-
-
Ohira, T.1
Milton, J.2
-
57
-
-
0001676780
-
Resonance with noise and delay
-
Ohira, T. and Sato, Y., Resonance with noise and delay, Phys. Rev. Lett. 82, 1999, 2811-2815.
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 2811-2815
-
-
Ohira, T.1
Sato, Y.2
-
58
-
-
0000255892
-
Delayed stochastic systems
-
Ohira, T. and Yamane, T., Delayed stochastic systems, Phys. Rev. E 61, 2000, 1247-1257.
-
(2000)
Phys. Rev. e
, vol.61
, pp. 1247-1257
-
-
Ohira, T.1
Yamane, T.2
-
59
-
-
0037093040
-
Predictability of currency market exchange
-
Ohira, T., Sazuka, N., Marumo, K., Shimizu, T., Takayasu, M. and Takayasu, H., Predictability of currency market exchange, Phys. A 308, 2002, 368-374.
-
(2002)
Phys. A
, vol.308
, pp. 368-374
-
-
Ohira, T.1
Sazuka, N.2
Marumo, K.3
Shimizu, T.4
Takayasu, M.5
Takayasu, H.6
-
60
-
-
33344463083
-
Theoretical analysis of destablization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control
-
Patanarapeelert, K., Frank, T. D., Friedrich, R., Beek, P. J. and Tang, I. M., Theoretical analysis of destablization resonances in time-delayed stochastic second-order dynamical systems and some implications for human motor control, Phys. Rev. E 73, 2006, 021901.
-
(2006)
Phys. Rev. e
, vol.73
, pp. 021901
-
-
Patanarapeelert, K.1
Frank, T.D.2
Friedrich, R.3
Beek, P.J.4
Tang, I.M.5
-
62
-
-
10244232264
-
-
Cambridge University Press, New York, NY
-
Rudnick, J. and Gaspari, G., Elements of the Random Walk, Cambridge University Press, New York, NY, 2004.
-
(2004)
Elements of the Random Walk
-
-
Rudnick, J.1
Gaspari, G.2
-
63
-
-
0035852686
-
Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data
-
Santillan, M. and Mackey, M. C., Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data, Proc. Natl Acad. Sci. 98, 2001, 1364-1369.
-
(2001)
Proc. Natl Acad. Sci.
, vol.98
, pp. 1364-1369
-
-
Santillan, M.1
Mackey, M.C.2
-
65
-
-
33646751002
-
Brownian motor with time-delayed feedback
-
Wu, D. and Zhu, S., Brownian motor with time-delayed feedback, Phys. Rev. E 73, 2006, 051107.
-
(2006)
Phys. Rev. e
, vol.73
, pp. 051107
-
-
Wu, D.1
Zhu, S.2
-
66
-
-
17744387337
-
Delayed stochastic differential equation model for quiet standing
-
Yao, W., Yu, P. and Essex, C., Delayed stochastic differential equation model for quiet standing, Phys. Rev. E 63, 2001, 021902.
-
(2001)
Phys. Rev. e
, vol.63
, pp. 021902
-
-
Yao, W.1
Yu, P.2
Essex, C.3
-
67
-
-
3042596483
-
Dynamics and stability in a reduced model of the lac operon
-
Yildirim, N., Santillan, M., Horik, D. and Mackey, M. C., Dynamics and stability in a reduced model of the lac operon, Chaos 14, 2004, 279-292.
-
(2004)
Chaos
, vol.14
, pp. 279-292
-
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Yildirim, N.1
Santillan, M.2
Horik, D.3
Mackey, M.C.4
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