-
1
-
-
79954562301
-
Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields
-
P. Aguirre, E. J. Doodol, B. Krauskopf and H. M. Osinga, Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields, Discr. Contin. Dynam. Syst., 29 (2011), 1309-1344.
-
(2011)
Discr. Contin. Dynam. Syst
, vol.29
, pp. 1309-1344
-
-
Aguirre, P.1
Doodol, E.J.2
Krauskopf, B.3
Osinga, H.M.4
-
2
-
-
33745292753
-
Crossing bifurcations and unstable dimension variability
-
K. T. Alligood, E. Sander and J. A. Yorko, Crossing bifurcations and unstable dimension variability, Phys. Rev. Lett., 96 (2006), 244103.
-
(2006)
Phys. Rev. Lett
, vol.96
, pp. 244103
-
-
Alligood, K.T.1
Sander, E.2
Yorko, J.A.3
-
3
-
-
0027421180
-
A single-pool model for intracellular calcium oscillations and waves in the xenopus laevis oocyte
-
A. Atri, J. Amundsen, D. Clapham and J. Sneyd, A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte, Biophysical Journal, 65 (1993), 17271739.
-
(1993)
Biophysical Journal
, vol.65
, pp. 17271739
-
-
Atri, A.1
Amundsen, J.2
Clapham, D.3
Sneyd, J.4
-
4
-
-
0001340513
-
The numerical computation of connecting orbits in dynamical systems
-
W.-J. Boyn, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 10 (1990), 379-405.
-
(1990)
IMA J. Numer. Anal
, vol.10
, pp. 379-405
-
-
Boyn, W.-J.1
-
5
-
-
0012912040
-
On well-posed problems for connecting orbits in dynamical systems
-
in "Chaotic Numerics" (Goolong, 1993), Amor. Math. Soc, Providence, RI
-
W.-J. Boyn, On well-posed problems for connecting orbits in dynamical systems, in "Chaotic Numerics" (Goolong, 1993), Cont. Math., 172, Amor. Math. Soc, Providence, RI, (1994), 131-168.
-
(1994)
Cont. Math
, vol.172
, pp. 131-168
-
-
Boyn, W.-J.1
-
6
-
-
0001842302
-
Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain
-
M. P. Boor, B. W. Kooi and S. A. L. M. Kooijman, Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain, J. Math. Biology, 39 (1999), 19-38.
-
(1999)
J. Math. Biology
, vol.39
, pp. 19-38
-
-
Boor, M.P.1
Kooi, B.W.2
Kooijman, S.A.L.M.3
-
7
-
-
0035109332
-
Multiple attractors and boundary crises in a tri-trophic food chain
-
M. P. Boor, B. W. Kooi and S. A. L. M. Kooijman, Multiple attractors and boundary crises in a tri-trophic food chain, Math. Bioscioncos, 169 (2001), 109-128.
-
(2001)
Math. Bioscioncos
, vol.169
, pp. 109-128
-
-
Boor, M.P.1
Kooi, B.W.2
Kooijman, S.A.L.M.3
-
9
-
-
7244225978
-
-
Mathematical Physics, III, Springer-Vorlag, Berlin
-
C. Bonatti, L. Diaz and M. Viana, "Dynamics Beyond Uniform Hyporbolicity. A Global Geometric and Probabilistic Perspective," Encyclopaedia of Mathematical Sciences, 102, Mathematical Physics, III, Springer-Vorlag, Berlin, 2005.
-
(2005)
Dynamics beyond Uniform Hyporbolicity. A Global Geometric and Probabilistic Perspective," Encyclopaedia of Mathematical Sciences
, vol.102
-
-
Bonatti, C.1
Diaz, L.2
Viana, M.3
-
10
-
-
47849112972
-
When shil'nikov meets hopf in excitable systems
-
A. R. Champneys, V. Kirk, E. Knobloch, B. E. Oldoman and J. Snoyd, When Shil'nikov Meets Hopf in excitable systems, SIAM J. Appl. Dynam. Syst., 6 (2007), 663-693.
-
(2007)
SIAM J. Appl. Dynam. Syst
, vol.6
, pp. 663-693
-
-
Champneys, A.R.1
Kirk, V.2
Knobloch, E.3
Oldoman, B.E.4
Snoyd, J.5
-
11
-
-
76149094233
-
Unfolding a tangent equilibrium-to-periodic heteroclinic cycle
-
A. R. Champnoys, E. Knobloch, V. Kirk, B. E. Oldoman and J. D. M. Radomachor, Unfolding a tangent equilibrium-to-periodic heteroclinic cycle, SIAM J. App. Dyn. Sys., 8 (2009), 12611304.
-
(2009)
SIAM J. App. Dyn. Sys
, vol.8
, pp. 12611304
-
-
Champnoys, A.R.1
Knobloch, E.2
Kirk, V.3
Oldoman, B.E.4
Radomachor, J.D.M.5
-
12
-
-
0030136339
-
A numerical toolbox for homoclinic bifurcation analysis
-
A. R. Champnoys, Yu. A. Kuznotsov and B. Sandstodo, A numerical toolbox for homoclinic bifurcation analysis, Int. J. Bif. Chaos Appl. Sci. Engrg., 6 (1996), 867-887.
-
(1996)
Int. J. Bif. Chaos Appl. Sci. Engrg
, vol.6
, pp. 867-887
-
-
Champnoys, A.R.1
Kuznotsov, Y.A.2
Sandstodo, B.3
-
13
-
-
0034456294
-
Computing connecting orbits via an improved algorithm for continuing invariant subspaces
-
J. W. Dommel, L. Dioci and M. J. Friedman, Computing connecting orbits via an improved algorithm for continuing invariant subspaces, SIAM J. Sci. Comput., 22 (2000), 81-94.
-
(2000)
SIAM J. Sci. Comput
, vol.22
, pp. 81-94
-
-
Dommel, J.W.1
Dioci, L.2
Friedman, M.J.3
-
14
-
-
58149362431
-
Šil'nikov-hopf bifurcations
-
B. Dong and K. Sakamoto, Šil'nikov-Hopf bifurcations, J. Diff. Eqns., 119 (1995), 1-23.
-
(1995)
J. Diff. Eqns
, vol.119
, pp. 1-23
-
-
Dong, B.1
Sakamoto, K.2
-
16
-
-
8744230577
-
Matcont: A matlab package for numerical bifurcation analysis of ODEs
-
A. Dhooge, W. Govaorts and Yu. A. Kuznotsov, MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans. Math. Software, 29 (2003), 141-164. Available at: http://www.matcont.ugent.be/.
-
(2003)
ACM Trans. Math. Software
, vol.29
, pp. 141-164
-
-
Dhooge, A.1
Govaorts, W.2
Kuznotsov Yu., A.3
-
17
-
-
0035587772
-
Partially hyperbolic and transitive dynamics generated by heteroclinic cycles
-
L. Diaz and J. Rocha, Partially hyperbolic and transitive dynamics generated by heteroclinic cycles, Ergod. Th. Dynam. Sys., 21 (2001), 25-76.
-
(2001)
Ergod. Th. Dynam. Sys
, vol.21
, pp. 25-76
-
-
Diaz, L.1
Rocha, J.2
-
20
-
-
84892356236
-
Lecture notes on numerical analysis of nonlinear equations, in
-
(ods. B. Krauskopf, H. M. Osinga and J. Galán-Vioque), Underst. Complex Syst., Springer, Dordrecht
-
E. J. Doodol, Lecture notes on numerical analysis of nonlinear equations, in "Numerical Continuation Methods for Dynamical Systems" (ods. B. Krauskopf, H. M. Osinga and J. Galán-Vioque), Underst. Complex Syst., Springer, Dordrecht, (2007), 1-49.
-
(2007)
Numerical Continuation Methods for Dynamical Systems
, pp. 1-49
-
-
Doodol, E.J.1
-
21
-
-
84962866297
-
-
with major contributions from A. R. Champnoys, T. F. Fairgriovo, Yu. A. Kuznetsov, B. E. Oldeman, R. C. Paffenroth, B. Sandstede, X. J. Wang and C. Zhang
-
E. J. Doodol, with major contributions from A. R. Champnoys, T. F. Fairgriovo, Yu. A. Kuznetsov, B. E. Oldeman, R. C. Paffenroth, B. Sandstede, X. J. Wang and C. Zhang, AUTO-07P: Continuation and bifurcation software for ordinary differential equations. Available at: http://cmvl.cs.concordia.ca/.
-
AUTO-07P: Continuation and Bifurcation Software for Ordinary Differential Equations
-
-
Doodol, E.J.1
-
22
-
-
0001058067
-
Numerical computation of heteroclinic orbits
-
E. J. Doodol and M. J. Friedman, Numerical computation of heteroclinic orbits, J. Comput. Appl. Math., 26 (1989), 155-170.
-
(1989)
J. Comput. Appl. Math
, vol.26
, pp. 155-170
-
-
Doodol, E.J.1
Friedman, M.J.2
-
23
-
-
52149091923
-
Continuation of connecting orbits in SD-ODES: I. Point-to-cycle connections
-
E. J. Doodol, B. W. Kooi, Yu. A. Kuznotsov and G. A. K. van Voorn, Continuation of connecting orbits in SD-ODES: I. Point-to-cycle connections, Int. J. Bifurc. Chaos Appl. Sci. Engrg., 18 (2008), 1889-1903.
-
(2008)
Int. J. Bifurc. Chaos Appl. Sci. Engrg
, vol.18
, pp. 1889-1903
-
-
Doodol, E.J.1
Kooi, B.W.2
Kuznotsov Yu., A.3
Van Voorn, G.A.K.4
-
24
-
-
65249145224
-
Continuation of connecting orbits in SD-ODES: II. Cycle-to-cycle connections
-
E. J. Doodol, B. W. Kooi, Yu. A. Kuznotsov and G. A. K. van Voorn, Continuation of connecting orbits in SD-ODES: II. Cycle-to-cycle connections, Int. J. Bifurc. Chaos Appl. Sei. Engrg., 19 (2009), 159-169.
-
(2009)
Int. J. Bifurc. Chaos Appl. Sei. Engrg
, vol.19
, pp. 159-169
-
-
Doodol, E.J.1
Kooi, B.W.2
Kuznotsov Yu., A.3
Van Voorn, G.A.K.4
-
25
-
-
33846058378
-
Global bifurcations of the lorenz manifold
-
E. J. Doodol, B. Krauskopf and H. M. Osinga, Global bifurcations of the Lorenz manifold, Nonlinoarity, 19 (2006), 2947-2972.
-
(2006)
Nonlinoarity
, vol.19
, pp. 2947-2972
-
-
Doodol, E.J.1
Krauskopf, B.2
Osinga, H.M.3
-
26
-
-
33644887198
-
Computing one-dimensional global manifolds of poincaré maps by continuation
-
DOI 10.1137/05062408X
-
J. P. England, B. Krauskopf and H. M. Osinga, Computing one-dimensional global manifolds of Poincaré maps by continuation, SIAM J. Appl. Dynam. Syst., 4 (2005), 1008-1041. (Pubitemid 43385157)
-
(2005)
SIAM Journal on Applied Dynamical Systems
, vol.4
, Issue.4
, pp. 1008-1041
-
-
England, J.P.1
Krauskopf, B.2
Osinga, H.M.3
-
27
-
-
3142773575
-
2+ signaling
-
2+ signaling, Adv. Phys., 53 (2004), 255-440.
-
(2004)
Adv. Phys
, vol.53
, pp. 255-440
-
-
Falcko, M.1
-
28
-
-
2742611797
-
A case study for homoclinic chaos in an autonomous electronic circuit
-
E. Freire, A. J. Rodriguez-Luis, E. Gamero and E. Ponce, A case study for homoclinic chaos in an autonomous electronic circuit: A trip from Takens-Bogdanov to Hopf-Sil'nikov, Physica D, 62 (1993), 230-253.
-
(1993)
A Trip from Takens-Bogdanov to Hopf-Sil'nikov, Physica D
, vol.62
, pp. 230-253
-
-
Freire, E.1
Rodriguez-Luis, A.J.2
Gamero, E.3
Ponce, E.4
-
29
-
-
0026170304
-
Numerical computation and continuation of invariant manifolds connecting fixed points
-
M. Friedman and E. J. Doodol, Numerical computation and continuation of invariant manifolds connecting fixed points, SIAM J. Numer. Anal., 28 (1991), 789-808. (Pubitemid 21650677)
-
(1991)
SIAM Journal on Numerical Analysis
, vol.28
, Issue.3
, pp. 789-808
-
-
Friedman, M.J.1
Doedel, E.J.2
-
30
-
-
2042442839
-
Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study
-
M. Friedman and E. J. Doodol, Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study, J. Dyn. Diff. Eq., 5 (1993), 37-57.
-
(1993)
J. Dyn. Diff. Eq
, vol.5
, pp. 37-57
-
-
Friedman, M.1
Doodol, E.J.2
-
32
-
-
80053346248
-
Multiple time-scales, mixed mode oscillations and canards in intracellular calcium models
-
E. Harvey, V. Kirk, J. Snoyd and M. Wochsolborgor, Multiple time-scales, mixed mode oscillations and canards in intracellular calcium models, J. Nonlinear Science, 21 (2011), 639-683.
-
(2011)
J. Nonlinear Science
, vol.21
, pp. 639-683
-
-
Harvey, E.1
Kirk, V.2
Snoyd, J.3
Wochsolborgor, M.4
-
33
-
-
0000036850
-
Šil'nikov-Hopf bifurcation
-
P. Hirschborg and E. Knobloch, Šil'nikov-Hopf bifurcation, Phys. D, 62 (1993), 202-216.
-
(1993)
Phys. D
, vol.62
, pp. 202-216
-
-
Hirschborg, P.1
Knobloch, E.2
-
34
-
-
77956987116
-
Homoclinic and heteroclinic bifurcations in vector fields
-
(ods. H. Broor, F. Takons and B. Hassolblatt), Elsevier
-
A. J. Homburg and B, Sandstodo, Homoclinic and heteroclinic bifurcations in vector fields, in "Handbook of Dynamical Systems III" (ods. H. Broor, F. Takons and B. Hassolblatt), Elsevier, (2010), 379-524.
-
(2010)
Handbook of Dynamical Systems III
, pp. 379-524
-
-
Homburg, A.J.1
Sandstodo, B.2
-
35
-
-
0242648399
-
Lin's method for discrete dynamical systems, J
-
J. Knobloch, Lin's method for discrete dynamical systems, J. Difference Equations and Applications, 6 (2000), 577-623.
-
(2000)
Difference Equations and Applications
, vol.6
, pp. 577-623
-
-
Knobloch, J.1
-
36
-
-
19944418492
-
Lin's method for discrete and continuous dynamical systems and applications
-
TU Ilmenau
-
J. Knobloch, "Lin's Method for Discrete and Continuous Dynamical Systems and Applications," Habilitationsschrift, TU Ilmenau, 2004.
-
(2004)
Habilitationsschrift
-
-
Knobloch, J.1
-
37
-
-
76149123202
-
Lin's method for heteroclinic chains involving periodic orbits
-
J. Knobloch and T. Rieß, Lin's method for heteroclinic chains involving periodic orbits, Nonlinoarity, 23 (2010), 23-54.
-
(2010)
Nonlinoarity
, vol.23
, pp. 23-54
-
-
Knobloch, J.1
Rieß, T.2
-
38
-
-
80051763599
-
Nonreversible homoclinic snaking
-
J. Knobloch, T, Rieß and M. Vielitz, Nonreversible homoclinic snaking, Dynamical Systems, 26 (2011), 335-365.
-
(2011)
Dynamical Systems
, vol.26
, pp. 335-365
-
-
Knobloch, J.1
Rieß, T.2
Vielitz, M.3
-
39
-
-
0002623916
-
Unstable dimension variability: A source of nonhyperbolicity in chaotic systems
-
PII S0167278997001619
-
E. J. Kostolich, I. Kan, C. Grobogi, E. Ott and J. A. Yorko, Unstable dimension variability: A source of nonhyperbolicity in chaotic systems, Physica D, 109 (1997), 81-90. (Pubitemid 127701567)
-
(1997)
Physica D: Nonlinear Phenomena
, vol.109
, Issue.1-2
, pp. 81-90
-
-
Kostelich, E.J.1
Kan, I.2
Grebogi, C.3
Ott, E.4
Yorke, J.A.5
-
40
-
-
33747418994
-
Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation
-
DOI 10.1088/0951-7715/19/9/010, PII S0951771506240027, 010
-
B. Krauskopf and B. E. Oldoman, Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation, Nonlinoarity, 19 (2006), 2149-2167. (Pubitemid 44249948)
-
(2006)
Nonlinearity
, vol.19
, Issue.9
, pp. 2149-2167
-
-
Krauskopf, B.1
Oldeman, B.E.2
-
41
-
-
57549119107
-
Numerical continuation methods for dynamical systems. Path following and boundary value problems
-
Eds., Springer, Dordrecht
-
B. Krauskopf, H. M. Osinga and J. Galán-Vioque, eds., "Numerical Continuation Methods for Dynamical Systems. Path Following and Boundary Value Problems," Understanding Complex Systems, Springer, Dordrecht, 2007.
-
(2007)
Understanding Complex Systems
-
-
Krauskopf, B.1
Osinga, H.M.2
Galán-Vioque, J.3
-
42
-
-
47849115552
-
A Lin's method approach to finding and continuing heteroclinic orbits connections involving periodic orbits
-
B. Krauskopf and T. Rieß, A. Lin's method approach to finding and continuing heteroclinic orbits connections involving periodic orbits, Nonlinoarity, 21 (2008), 1655-1690.
-
(2008)
Nonlinoarity
, vol.21
, pp. 1655-1690
-
-
Krauskopf, B.1
Rieß, T.2
-
44
-
-
0036252851
-
Belyakov homoclinic bifurcations in a tritrophic food chain model
-
PII S0036139900378542
-
Yu. A. Kuznotsov, O. Do Feo and S. Rinaldi, Belyakov homoclinic bifurcations in a tritrophic food-chain model, SIAM J. Appl. Math., 62 (2001), 462-487. (Pubitemid 33779885)
-
(2001)
SIAM Journal on Applied Mathematics
, vol.62
, Issue.2
, pp. 462-487
-
-
Kuznetsov, Y.A.1
De Feo, O.2
Rinaldi, S.3
-
45
-
-
84972438215
-
Using mel'nikov's method to solve šil'nikov's problems
-
X.-B. Lin, Using Mel'nikov's method to solve Šil'nikov's problems, Proc. R. Soc. Edinb. Sect. A, 116 (1990), 295-325.
-
(1990)
Proc. R. Soc. Edinb. Sect. A
, vol.116
, pp. 295-325
-
-
Lin, X.-B.1
-
46
-
-
0346280077
-
Homoclinic branch switching: A numerical implementation of Lin's method
-
DOI 10.1142/S0218127403008326
-
B. E. Oldoman, A. R. Champnoys and B. Krauskopf, Homoclinic branch switching: A numerical implementation of Lin's method, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 13 (2003), 2977-2999. (Pubitemid 38034501)
-
(2003)
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
, vol.13
, Issue.10
, pp. 2977-2999
-
-
Oldeman, B.E.1
Champneys, A.R.2
Krauskopf, B.3
-
47
-
-
0003633463
-
-
An Introduction, Translated from the Portuguese by A. K. Manning, Springer-Vorlag, New York-Berlin
-
J. Palis, Jr., and W. do Melo, "Geometric Theory of Dynamical Systems. An Introduction," Translated from the Portuguese by A. K. Manning, Springer-Vorlag, New York-Berlin, 1982.
-
(1982)
Geometric Theory of Dynamical Systems
-
-
Palis Jr., J.1
Do Melo, W.2
-
48
-
-
0035545015
-
Numerical approximation of connecting orbits with asymptotic rate
-
T. Pampol, Numerical approximation of connecting orbits with asymptotic rate, Numerische Mathematik, 90 (2001), 309-348.
-
(2001)
Numerische Mathematik
, vol.90
, pp. 309-348
-
-
Pampol, T.1
-
49
-
-
27744536022
-
Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit
-
J. D. M. Radomachor, Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit, J. Diff. Eqns., 218 (2005), 390-443.
-
(2005)
J. Diff. Eqns
, vol.218
, pp. 390-443
-
-
Radomachor, J.D.M.1
-
50
-
-
77952642583
-
Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies
-
J. D. M. Radomachor, Lyapunov-Schmidt reduction for unfolding heteroclinic networks of equilibria and periodic orbits with tangencies, J. Diff. Eqns., 249 (2010), 305-348.
-
(2010)
J. Diff. Eqns
, vol.249
, pp. 305-348
-
-
Radomachor, J.D.M.1
-
53
-
-
24144495753
-
Bifurcations of n-homoclinic orbits in optically injected lasers
-
DOI 10.1088/0951-7715/18/3/010
-
S. M. Wioczorok and B. Krauskopf, Bifurcations of n-homoclinic orbits in optically injected lasers, Nonlinoarity, 18 (2005), 1095-1120. (Pubitemid 43033007)
-
(2005)
Nonlinearity
, vol.18
, Issue.3
, pp. 1095-1120
-
-
Wieczorek, S.1
Krauskopf, B.2
-
54
-
-
0010765318
-
Multipulses of nonlinearly-coupled Schrödinger equations
-
A. C. Yew, Multipulses of nonlinearly-coupled Schrödinger equations, J. Diff. Eqns., 173 (2001), 92-137.
-
(2001)
J. Diff. Eqns
, vol.173
, pp. 92-137
-
-
Yew, A.C.1
-
55
-
-
84859739166
-
Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales
-
W. Zhang, V. Kirk, J. Snoyd and M. Wochsolborgor, Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales, J. Math. Nouroscionco, 1 (2011).
-
(2011)
J. Math. Nouroscionco
, vol.1
-
-
Zhang, W.1
Kirk, V.2
Snoyd, J.3
Wochsolborgor, M.4
|