-
1
-
-
0003595232
-
-
Springer-Verlag, New York, Heidelberg, Berlin
-
V. ARNOLD, Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1983.
-
(1983)
Geometrical Methods in the Theory of Ordinary Differential Equations
-
-
Arnold, V.1
-
3
-
-
0008998664
-
The bifurcation set in a system with a homoclinic saddle curve
-
L. BELYAKOV, The bifurcation set in a system with a homoclinic saddle curve, Mat. Zametki, 28 (1981), pp. 910-916.
-
(1981)
Mat. Zametki
, vol.28
, pp. 910-916
-
-
Belyakov, L.1
-
4
-
-
0031749033
-
Food chain dynamics in the chemostat
-
M. BOER, B. KOOI, AND S. KOOIJMAN, Food chain dynamics in the chemostat, Math. Biosci., 150 (1998), pp. 43-62.
-
(1998)
Math. Biosci.
, vol.150
, pp. 43-62
-
-
Boer, M.1
Kooi, B.2
Kooijman, S.3
-
5
-
-
0001842302
-
Homoclinic and heteroclinic orbits in a tri-trophic food chain
-
M. BOER, B. KOOI, AND S. KOOIJMAN, Homoclinic and heteroclinic orbits in a tri-trophic food chain, J. Math. Biol., 39 (1999), pp. 19-38.
-
(1999)
J. Math. Biol.
, vol.39
, pp. 19-38
-
-
Boer, M.1
Kooi, B.2
Kooijman, S.3
-
6
-
-
21844486228
-
Numerical detection and continuation of codimension-two homoclinic bifurcations
-
A. CHAMPNEYS AND Y. KUZNETSOV, Numerical detection and continuation of codimension-two homoclinic bifurcations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 4 (1994), pp. 795-822.
-
(1994)
Internat. J. Bifur. Chaos Appl. Sci. Engrg.
, vol.4
, pp. 795-822
-
-
Champneys, A.1
Kuznetsov, Y.2
-
7
-
-
0030136339
-
A numerical toolbox for homoclinic bifurcation analysis
-
A. CHAMPNEYS, Y. KUZNETSOV, AND B. SANDSTEDE, A numerical toolbox for homoclinic bifurcation analysis, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 6 (1996), pp. 867-887.
-
(1996)
Internat. J. Bifur. Chaos Appl. Sci. Engrg.
, vol.6
, pp. 867-887
-
-
Champneys, A.1
Kuznetsov, Y.2
Sandstede, B.3
-
8
-
-
46549093797
-
Chaos in a three variable model of an excitable cell
-
T. CHAY, Chaos in a three variable model of an excitable cell, Phys. D, 16 (1985), pp. 233-242.
-
(1985)
Phys. D
, vol.16
, pp. 233-242
-
-
Chay, T.1
-
9
-
-
0001747368
-
Uniqueness of a limit cycle of a predator-prey system
-
K. CHENG, Uniqueness of a limit cycle of a predator-prey system, SIAM J. Math. Anal., 12 (1981), pp. 541-548.
-
(1981)
SIAM J. Math. Anal.
, vol.12
, pp. 541-548
-
-
Cheng, K.1
-
10
-
-
0039010341
-
The Colpitts oscillator: Families of periodic solutions and their bifurcations
-
O. DE FEO, G. M. MAGGIO, AND M. P. KENNEDY, The Colpitts oscillator: Families of periodic solutions and their bifurcations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 10 (2000), pp. 935-958.
-
(2000)
Internat. J. Bifur. Chaos Appl. Sci. Engrg.
, vol.10
, pp. 935-958
-
-
De Feo, O.1
Maggio, G.M.2
Kennedy, M.P.3
-
11
-
-
0030856091
-
Yield and dynamics of tritrophic food chains
-
O. DE FEO AND S. RINALDI, Yield and dynamics of tritrophic food chains, Am. Nat., 150 (1997), pp. 328-345.
-
(1997)
Am. Nat.
, vol.150
, pp. 328-345
-
-
De Feo, O.1
Rinaldi, S.2
-
12
-
-
0032004760
-
Singular homoclinic bifurcations in tri-trophic food chains
-
O. DE FEO AND S. RINALDI, Singular homoclinic bifurcations in tri-trophic food chains, Math. Biosci., 148 (1998), pp. 7-20.
-
(1998)
Math. Biosci.
, vol.148
, pp. 7-20
-
-
De Feo, O.1
Rinaldi, S.2
-
13
-
-
0023116926
-
From simple to complex oscillatory behaviour: Analysis of bursting in a multiply regulated biochemical system
-
O. DECROLY AND A. GOLDBETER, From simple to complex oscillatory behaviour: Analysis of bursting in a multiply regulated biochemical system, J. Theoret. Biol., 124 (1987), pp. 219-250.
-
(1987)
J. Theoret. Biol.
, vol.124
, pp. 219-250
-
-
Decroly, O.1
Goldbeter, A.2
-
14
-
-
0003487030
-
-
Computer Science, Concordia University, Montreal, QC
-
E. DOEDEL, A. CHAMPNEYS, T. FAIRGRIEVE, Y. KUZNETSOV, B. SANDSTEDE, AND X. WANG, AUTO97: Continuation and bifurcation software for ordinary differential equations (with HOMCONT). Computer Science, Concordia University, Montreal, QC, 1997.
-
(1997)
AUTO97: Continuation and Bifurcation Software for Ordinary Differential Equations (With HOMCONT)
-
-
Doedel, E.1
Champneys, A.2
Fairgrieve, T.3
Kuznetsov, Y.4
Sandstede, B.5
Wang, X.6
-
15
-
-
0001477332
-
Double impulse solutions in nerve axon equations
-
J. EVANS, N. FENICHEL, AND J. FEROE, Double impulse solutions in nerve axon equations, SIAM J. Appl. Math., 42 (1982), pp. 219-234.
-
(1982)
SIAM J. Appl. Math.
, vol.42
, pp. 219-234
-
-
Evans, J.1
Fenichel, N.2
Feroe, J.3
-
16
-
-
0000110568
-
A nonlinear dynamical model for the dynastic cycle
-
G. FEICHTINGER, C. FORST, AND C. PICCARDI, A nonlinear dynamical model for the dynastic cycle, Chaos Solitons Fractals, 7 (1996), pp. 257-271.
-
(1996)
Chaos Solitons Fractals
, vol.7
, pp. 257-271
-
-
Feichtinger, G.1
Forst, C.2
Piccardi, C.3
-
17
-
-
0002808656
-
Global stability and persistence of simple food chains
-
H. FREEDMAN AND J. SO, Global stability and persistence of simple food chains, Math. Biosci., 76 (1985), pp. 69-86.
-
(1985)
Math. Biosci.
, vol.76
, pp. 69-86
-
-
Freedman, H.1
So, J.2
-
18
-
-
0017407813
-
Mathematical analysis of some three-species food-chain models
-
H. FREEDMAN AND P. WALTMAN, Mathematical analysis of some three-species food-chain models, Math. Biosci., 33 (1977), pp. 257-276.
-
(1977)
Math. Biosci.
, vol.33
, pp. 257-276
-
-
Freedman, H.1
Waltman, P.2
-
19
-
-
0019059241
-
Persistence in food chains with general interactions
-
T. GARD, Persistence in food chains with general interactions, Math. Biosci., 51 (1980), pp. 165-174.
-
(1980)
Math. Biosci.
, vol.51
, pp. 165-174
-
-
Gard, T.1
-
20
-
-
0021442615
-
Bifurcation phenomena near homoclinic systems: A two-parameter analysis
-
P. GASPARD, R. KAPRAL, AND G. NICOLIS, Bifurcation phenomena near homoclinic systems: A two-parameter analysis, J. Statist. Phys., 35 (1984), pp. 697-727.
-
(1984)
J. Statist. Phys.
, vol.35
, pp. 697-727
-
-
Gaspard, P.1
Kapral, R.2
Nicolis, G.3
-
21
-
-
0021437639
-
Local and global behavior near homoclinic orbits
-
P. GLENDINNING AND C. SPARROW, Local and global behavior near homoclinic orbits, J. Statist. Phys., 35 (1984), pp. 645-696.
-
(1984)
J. Statist. Phys.
, vol.35
, pp. 645-696
-
-
Glendinning, P.1
Sparrow, C.2
-
22
-
-
0000617778
-
Complexity in the bifurcation structure of homoclinic loops to a saddle-focus
-
S. GONCHENKO, D. TURAEV, P. GASPARD, AND G. NICOLIS, Complexity in the bifurcation structure of homoclinic loops to a saddle-focus, Nonlinearity, 10 (1997), pp. 409-423.
-
(1997)
Nonlinearity
, vol.10
, pp. 409-423
-
-
Gonchenko, S.1
Turaev, D.2
Gaspard, P.3
Nicolis, G.4
-
23
-
-
0009086857
-
Food chains in the chemostat: Relationships between mean yield and complex dynamics
-
A. GRAGNANI, O. DE FEO, AND S. RINALDI, Food chains in the chemostat: Relationships between mean yield and complex dynamics, Bull. Math. Biol., 1 (1998), pp. 1-16.
-
(1998)
Bull. Math. Biol.
, vol.1
, pp. 1-16
-
-
Gragnani, A.1
De Feo, O.2
Rinaldi, S.3
-
24
-
-
0025956240
-
Chaos in a three-species food chain
-
A. HASTINGS AND T. POWELL, Chaos in a three-species food chain, Ecol., 72 (1991), pp. 896-903.
-
(1991)
Ecol.
, vol.72
, pp. 896-903
-
-
Hastings, A.1
Powell, T.2
-
25
-
-
0018146144
-
Interactive instruction on population interactions
-
P. HOGEWEG AND B. HESPER, Interactive instruction on population interactions, Comp. Biol. Med., 8 (1978), pp. 319-327.
-
(1978)
Comp. Biol. Med.
, vol.8
, pp. 319-327
-
-
Hogeweg, P.1
Hesper, B.2
-
26
-
-
0033591199
-
The effect of slow allosteric transitions in a coupled biochemical oscillator model
-
M. KÆRN AND A. HUNDING, The effect of slow allosteric transitions in a coupled biochemical oscillator model, J. Theoret. Biol., 198 (1999), pp. 269-281.
-
(1999)
J. Theoret. Biol.
, vol.198
, pp. 269-281
-
-
Kærn, M.1
Hunding, A.2
-
27
-
-
4544313738
-
Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps
-
A. KHIBNIK, Y. KUZNETSOV, V. LEVITIN, AND E. NIKOLAEV, Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps, Phys. D, 62 (1993), pp. 360-371.
-
(1993)
Phys. D
, vol.62
, pp. 360-371
-
-
Khibnik, A.1
Kuznetsov, Y.2
Levitin, V.3
Nikolaev, E.4
-
28
-
-
84951601313
-
Chaos in three species food chains
-
A. KLEBANOFF AND A. HASTINGS, Chaos in three species food chains, J. Math. Biol., 32 (1994), pp. 427-451.
-
(1994)
J. Math. Biol.
, vol.32
, pp. 427-451
-
-
Klebanoff, A.1
Hastings, A.2
-
29
-
-
0001913572
-
Complex dynamic behavior of autonomous microbial food chains
-
B. KOOI, M. BOER, AND S. KOOIJMAN, Complex dynamic behavior of autonomous microbial food chains, J. Math. Biol., 36 (1997), pp. 24-40.
-
(1997)
J. Math. Biol.
, vol.36
, pp. 24-40
-
-
Kooi, B.1
Boer, M.2
Kooijman, S.3
-
30
-
-
0032212732
-
Consequences of population models on the dynamics of food chains
-
B. KOOI, M. BOER, AND S. KOOIJMAN, Consequences of population models on the dynamics of food chains, Math. Biosci., 153 (1998), pp. 99-124.
-
(1998)
Math. Biosci.
, vol.153
, pp. 99-124
-
-
Kooi, B.1
Boer, M.2
Kooijman, S.3
-
31
-
-
0003687338
-
-
Springer-Verlag, New York, Berlin, Heidelberg
-
Y. KUZNETSOV, Elements of Applied Bifurcation Theory, Springer-Verlag, New York, Berlin, Heidelberg, 1995, 1998.
-
(1995)
Elements of Applied Bifurcation Theory
-
-
Kuznetsov, Y.1
-
33
-
-
0029663443
-
Remarks on food chain dynamics
-
Y. KUZNETSOV AND S. RINALDI, Remarks on food chain dynamics, Math. Biosci., 134 (1996), pp. 1-33.
-
(1996)
Math. Biosci.
, vol.134
, pp. 1-33
-
-
Kuznetsov, Y.1
Rinaldi, S.2
-
35
-
-
0039645998
-
Limit cycles in predator-prey communities
-
R. MAY, Limit cycles in predator-prey communities, Science, 177 (1972), pp. 900-902.
-
(1972)
Science
, vol.177
, pp. 900-902
-
-
May, R.1
-
36
-
-
0028035790
-
Biological conditions for chaos in a three-species food chain
-
K. MCCANN AND P. YODZIS, Biological conditions for chaos in a three-species food chain, Ecol., 75 (1994), pp. 561-564.
-
(1994)
Ecol.
, vol.75
, pp. 561-564
-
-
Mccann, K.1
Yodzis, P.2
-
37
-
-
0029479690
-
Bifurcation structure of a three-species food chain model
-
K. MCCANN AND P. YODZIS, Bifurcation structure of a three-species food chain model, Theor. Pop. Biol., 48 (1995), pp. 93-125.
-
(1995)
Theor. Pop. Biol.
, vol.48
, pp. 93-125
-
-
Mccann, K.1
Yodzis, P.2
-
38
-
-
0026169197
-
A separation condition for the existence of limit cycles in slow-fast systems
-
S. MURATORI AND S. RINALDI, A separation condition for the existence of limit cycles in slow-fast systems, Appl. Math. Model., 15 (1991), pp. 312-318.
-
(1991)
Appl. Math. Model.
, vol.15
, pp. 312-318
-
-
Muratori, S.1
Rinaldi, S.2
-
39
-
-
0027072404
-
Low- and high-frequency oscillations in three-dimensional food chain systems
-
S. MURATORI AND S. RINALDI, Low- and high-frequency oscillations in three-dimensional food chain systems, SIAM J. Appl. Math., 52 (1992), pp. 1688-1706.
-
(1992)
SIAM J. Appl. Math.
, vol.52
, pp. 1688-1706
-
-
Muratori, S.1
Rinaldi, S.2
-
40
-
-
0030320205
-
On the role of body size in a tri-trophic metapopulation model
-
S. RINALDI, S. DAL BO, AND E. DE NITTIS, On the role of body size in a tri-trophic metapopulation model, J. Math. Biol., 35 (1996), pp. 158-176.
-
(1996)
J. Math. Biol.
, vol.35
, pp. 158-176
-
-
Rinaldi, S.1
Dal Bo, S.2
De Nittis, E.3
-
41
-
-
0023791327
-
Emergence of organized bursting in clusters of pancreaic α-cells by channel sharing
-
A. SHERMAN, J. RINZER, AND J. KEUZER, Emergence of organized bursting in clusters of pancreaic α-cells by channel sharing, Biophys. J., 54 (1988), pp. 411-425.
-
(1988)
Biophys. J.
, vol.54
, pp. 411-425
-
-
Sherman, A.1
Rinzer, J.2
Keuzer, J.3
-
42
-
-
0002604954
-
Variazioni e fluttuazioni del numero di individui in specie animali conviventi
-
in Italian
-
V. VOLTERRA, Variazioni e fluttuazioni del numero di individui in specie animali conviventi, Mem. Accad. Lincei, 2 (1926), pp. 31-113 (in Italian).
-
(1926)
Mem. Accad. Lincei
, vol.2
, pp. 31-113
-
-
Volterra, V.1
|