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Grasman J. — Asymptotic methods for relaxation oscillations and applications
Grasman J. — Asymptotic methods for relaxation oscillations and applications

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Название: Asymptotic methods for relaxation oscillations and applications

Автор: Grasman J.

Аннотация:

The book deals with the symptotic analysis of relaxation oscillations, which are nonlinear oscillations characterized by rapid change of a variable within a short time interval of the cycle. The type of asymptotic approximation of the solution is known as the method of matched asymptotic expansions. In case of coupled oscillations it gives conditions for entrainment. For spatially distributed oscillators phase wave solutions can be constructed. The asymptotic theory also covers the chaotic dynamics of free and forced oscillations. The influence of stochastic perturbations upon the period of the oscillation is also covered. It is the first book on this subject which also provides a survey of the literature, reflecting historical developments in the field. Furthermore, relaxation oscillations are analyzed using the tools drawn from modern dynamical system theory. This book is intended for graduate students and researchers interested in the modelling of periodic phenomena in physics and biology and will provide a second knowledge of the application of the theory of nonlinear oscillations to a particular class of problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 223

Добавлена в каталог: 07.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airy function      39 55 57 61 163 187
Allen, T.      15 201
Alseda, LI      158 201
Amplitude      33 67 70
Anand, K.K.      15 201
Andersen, C.M      71 201 203
Anderson, P.M.      117 201
Annulus mapping      158
Argdmi, J      103 201
Asymptotic, ordering      189
Asymptotic, sequence      189
Auchmuty, J.F.G.      150 201
Averaging, condition      174
Averaging, method      122
Backward Kolmogorov equation      106 114 198
Barts, P      208
Bavinck, H.      67 201
Belair, J.      25 201
Belousov — Zhabotinsky reaction      8 87 89 99
Bifurcation      194
Biological system      139
Blevins, R.D.      117 201
Blom, J.G.      17 201
Bogoliubov, N.N.      1 74 117 201
Bojadziev, G.      8 201
Bonhoeffer, K.F      92 201
Bonhoeffer-Van der Pol equation      92
Boundary layer      12 25
Boundary layer, initial      35 41
Brandstatter, J.J      117 202
Broos, G      213
Brouwer’s fixed point theorem      41
Brunner, T.O      204
Brusselator      78
Callot, J — L.      25 202
Canard      42 94
Cantor set      114 156 184 193
Cardiac arrythmia      140
Carrier, G.F      56 202
Cartwright, M.L.      52 55 153 202
Catastrophe theory      9
Chain of oscillators      141
Chance, B      87 202
Chaos      112
Chaos, hidden      101
Chaotic solution      15 99 153
Chapman — Kolmogorov equation      196
Chemical reaction      8 20 87
Chow, P — L.      20 202
Circadian rhythm      8 17
Circle mapping      158
Clenshaw, C.W.      71 202
Climate fluctuations      7
Cohen, A.H.      131 202
Cole, J.D.      2 56 161 173 199 206
Collet, P.      101 159 202
Conservation function      8 20
Consonance      15
Conveyor-belt      6
Copson, E.T.      79 202
Coupling      19 22 121 131 144
Coupling with delay      122 130 135
Coupling, diffusion type of      20 139
Cronin, J      25 202
Crutchfield, J.P      15 203
Dadfar, M.B.      71 203
Danley, B.G.      204
De Bruin, R.      201
Degree of freedom      1
Deprit, A      71 203
Diener, F      25 94 202 203
Diener, M      94 202
Diffusion process      198
DIP      167 179
Dissipation function      8 20
Dmitriev, A.S      153 203
Dorodnicyn, A.A.      55 59 203
Duffing - Van der Pol oscillator      105
Dutt, r.      74 203
Dvorrak, I.      44 210
Dynamical system      190
Earthquake      7 130
Ebeling, W      8 15 105 203
Eckhaus, W      2 25 34 94 98 190 203
Eckmann, J — P.      101 159 202
El — Abbasy, E.M.      170 203
Electronic circuit      2 16 19 21
energy equation      52
Engel — Herbert, H      101 203
Entrainment      15
Entrainment, mutual      144
Entrainment, n:m      136 138 140 143
Equilibrium      192
Ermentrout, G.B.      93 140 141 144 203 206
Euler constant      85
Excitability      91
Expansion, asymptotic      189
Expansion, composite      14
Expansion, inner      13
Expansion, matched asymptotic      2 12 34
Expansion, outer      13
Expansion, regular      41
Expansion, two variables      161 173
Extension theorem      34
Farey fraction      15
Fast variable      10
Fibrillation      20 148
Fife, P.C.      20 203
Fire flie      18
Fitzhugh — Nagumo equations      92
Fitzhugh, R.      92 203
Flaherty, J.E      170 178 204
Flanders, D.A.      30 204
Fokker - Planck equation      197
Forcing, constant      91
Forcing, periodic      15 119 159 195
Forcing, sinusoidal      151
Forward Kolmogorov equation      197
Fouad, A.A      117 201
Franck, U.F      20 204
Gamma function      84 188
Gardiner, C.W      105 204
Gastro-intestinal tract      117
Geer, J      71 201 203
geyser      7
Ghosh, E.K.      202
Glass, L      17 131 140 205
Glycolytic oscillation      87
Goldbeter , A.      87 94 204
Gollub, J.P.      15 19 139 204
Gradient system      9
Grasman, J      15 67 76 103 141 160 170 180 182 201 204 205
Guckenheimer, J.      99 121 122 153 158 194 205
Guevara, M.R      17 205
Haag, J.      28 205
Habets, P      154 205
Hagendom, P.      117 205
Hahn, H.S.      94 105 205
Hamiltonian system      8 74
Hanson, F.E      18 205
Hayashi, C      7 15 117 205
Heart      8 17 20 118
Henon, M      194 205
Hess, B      202
Hidden, chaos      101
Hidden, component      101
Hill, A.V.      5 206
Hirakawa, K      206
Holden, A.V      8 206
Holmes, P.      25 99 153 158 194 201 202 205
Honerkamp, J      148 206 211
Hopf bifurcation      88 91 194
Hoppensteadt, F.C.      118 170 180
Horse-shoe map      48 153 193
Howard, L.N      91 211
Huberman, B.A      203
Implicit function theorem      78
Ince, E.      213
Interval mapping      159 183
Intestines      8 20 117
Invariant      191
Inverse gaussian distribution      109
Inverse Laplace asymptotics      85
Iooss, G.      194 206
Iteration mapping      18 99 120 191
Ito, K      7 103 206
Jaeger, N.I.      87 210
James, E.M      170 203
Jansen, M.J.W.      123 142 160 204 206
Johannesma, P.I.M.      8 206
Joseph, D.D.      194 206
Josephson junction      7
Kaplan, B.Z      7 206
Kaplun, S.      25 34
Karlin, S.      109 206
Keener, J.P.      118 140 206
Keith, W.L.      140 206
Kevorkian, J.      2 56 161 173 190 206
Kitney, R.I      207
Kohda, A.      210
Kokubu, H.      103 209
Kopell, N      93 141 206
Kreifeldt, J      143 206
Krogdahl, W.S.      71 206
Kune, R.D.      91 207
Kuramoto, Y      20 143 148 207
La Salle, J.      30 207
Large parameter      2 26
Lauwerier, H.A      76 99 207
Le Corbeiller,Ph      2 207
Leaving point      11 43
Levi, M      15 153 185 207
Levinson, D.      30 207
Lewis, J.A      56 202
Lienard plane      26 67
Lienard, A.      27 207
Limit cycle      192
Limit point      191
Linan, A      20 201
Linkens, D.A.      117 207
Littlewood, J.E.      153 202 207
Llibre, J.      201
Lloyd, N.G.      154 208
Logistic map      99 101
Lopes da Silva, F.H      143 206
Lorenz equations      99
Lorenz, E.N.      99 101 208
Lotka, A.J.      73 208
Lozi, R      99 103 208
Lyapunov, exponent      103
Lyapunov, stability      29
Mac Gillivray, A.D.      56 208
Mackey, M.C      131 204
Maess, G      71 208
Manifold      191
Manifold, stable      11 25 41
Markov process      196
Martz, H.F.      109 208
Matching      14 60
Matisoo, J      17 208
Matsumoto, K.      101 114 208
May, R.M.      101 208
Mayeri, E.      139 208
Message function      20
Metabolism      8
Minorsky, N.      70 117 208
Mishchenko, E.F.      25 42 51 119 125 208 209 213
Mitropolsky, I.A      1 74 117 201
Mitsui, T      71 209 210
Mook, D.T.      117 122 209
Moser, J      175 209
Musical scale      15
Mutscher, G.      206
Nagumo, J.      213
Nayfeh, A.H.      117 122 209
Nearest neighbour coupling      19
Nerve excitation      92 103
Neu, J.C      139 209
Neumann, D.A.      34 209
Neural oscillator      143
Newhouse, S.      158 185 209
Nicolis, G      87 91 150 201 209
Nijmeijer, H      204
Nipp, K      25 35 37 44 91 209
Nitzan, A      205
Noise      99 112
Nonlinear diffusion equation      20 148
Nonstandard analysis      25
North, G.R.      7 209
Oka, H      103 209
Oono, Y      206
Orbital stability      117
Order function      189
Oregonator      89
Ortolevan,P.      205
Osada, H.      213
Oscillation, almost linear      1 117
Oscillation, biochemical      8 87
Oscillation, chaotic      101
Oscillation, forced      15
Oscillation, harmonic      4 9 22 74
Oscillation, relaxation      2
Oscillation, self-sustained      2 27
Oscillation, stochastic      105
Oscillator, cardiac      8
Oscillator, damped      9
Oscillator, piece-wise linear      132 139
Oscillator, thermal      6
Othmer, H.G.      144 210
O’ Malley, R.E.      2 56 209
Pacemaker      17 134
Packard, N.H.      203
Palis, J.      158 185 209
Parabolic cylinder function      172 188
Perez, R      140 204
Period      12 34 52 67 70 82
Period, doubling      101 194
Periodic input      15
Phase      17 125 196
Phase, diffusion equation      148
Phase, fixation      141
Phase, locking      15
Phase, shift function      121 131 134
Phase, space      190
Phase, wave      19
Physical plane      56
Pitchfork bifurcation      194
Plateau’s of phase velocities      141
Poincare mapping      48 99 124 154
Poincare — Bendixson theorem      25 28 42
Pontryagin, L.S.      25 42 210
Ponzo, P.J.      30 33 71 210
Population cycle      5 9 17
Power spectrum      112 114
Prey-predator system      8 20 72
Prigogine, I      87 94 204
Radial isochron clock      117
Rand, R.H.      131 140 202 206 211
Random perturbation      101
Rayleigh equation      26
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