-
1
-
-
0016754941
-
Bifurcation analysis of nonlinear reaction-diffusion equations I: Evolution equations and the steady state solutions
-
Auchmuty J.F.G., and Nicolis G. Bifurcation analysis of nonlinear reaction-diffusion equations I: Evolution equations and the steady state solutions. Bull. Math. Biol. 37 (1975) 323-365
-
(1975)
Bull. Math. Biol.
, vol.37
, pp. 323-365
-
-
Auchmuty, J.F.G.1
Nicolis, G.2
-
2
-
-
0038778726
-
Global bifurcation in the Brusselator system
-
Brown K.J., and Davidson F.A. Global bifurcation in the Brusselator system. Nonlinear Anal. 12 (1995) 1713-1725
-
(1995)
Nonlinear Anal.
, vol.12
, pp. 1713-1725
-
-
Brown, K.J.1
Davidson, F.A.2
-
3
-
-
0346072299
-
Pattern formation in three-dimensional reaction-diffusion systems
-
Callahan T.K., and Knobloch E. Pattern formation in three-dimensional reaction-diffusion systems. Phys. D 132 (1999) 339-362
-
(1999)
Phys. D
, vol.132
, pp. 339-362
-
-
Callahan, T.K.1
Knobloch, E.2
-
4
-
-
84972537529
-
Existence and uniqueness of coexistence states for a predator-prey model with diffusion
-
Casal A., Eilbeck J.C., and López-Gómez J. Existence and uniqueness of coexistence states for a predator-prey model with diffusion. Differential Integral Equations 7 (1994) 411-439
-
(1994)
Differential Integral Equations
, vol.7
, pp. 411-439
-
-
Casal, A.1
Eilbeck, J.C.2
López-Gómez, J.3
-
5
-
-
1542720931
-
Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model
-
Chen W.Y., and Peng R. Stationary patterns created by cross-diffusion for the competitor-competitor-mutualist model. J. Math. Anal. Appl. 291 (2004) 550-564
-
(2004)
J. Math. Anal. Appl.
, vol.291
, pp. 550-564
-
-
Chen, W.Y.1
Peng, R.2
-
6
-
-
41449113551
-
Sharp estimates on minimum traveling wave speed of reaction-diffusion systems modeling autocatalysis
-
Chen X., and Qi Y. Sharp estimates on minimum traveling wave speed of reaction-diffusion systems modeling autocatalysis. SIAM J. Math. Anal. 39 (2007) 437-448
-
(2007)
SIAM J. Math. Anal.
, vol.39
, pp. 437-448
-
-
Chen, X.1
Qi, Y.2
-
7
-
-
0000814522
-
A counter example of competing species equations
-
Dancer E.N. A counter example of competing species equations. Differential Integral Equations 9 (1996) 239-246
-
(1996)
Differential Integral Equations
, vol.9
, pp. 239-246
-
-
Dancer, E.N.1
-
8
-
-
0033634578
-
On the symbiotic Lotka-Volterra model with diffusion and transport effects
-
Delgado M., López-Gómez J., and Suarez A. On the symbiotic Lotka-Volterra model with diffusion and transport effects. J. Differential Equations 160 (2000) 175-262
-
(2000)
J. Differential Equations
, vol.160
, pp. 175-262
-
-
Delgado, M.1
López-Gómez, J.2
Suarez, A.3
-
9
-
-
21744459836
-
Some uniqueness and exact multiplicity results for a predator-prey model
-
Du Y.H., and Lou Y. Some uniqueness and exact multiplicity results for a predator-prey model. Trans. Amer. Math. Soc. 349 (1997) 2443-2475
-
(1997)
Trans. Amer. Math. Soc.
, vol.349
, pp. 2443-2475
-
-
Du, Y.H.1
Lou, Y.2
-
10
-
-
23044527512
-
Qualitative behavior of positive solutions of a predator-prey model: effects of saturation
-
Du Y.H., and Lou Y. Qualitative behavior of positive solutions of a predator-prey model: effects of saturation. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 321-349
-
(2001)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.131
, pp. 321-349
-
-
Du, Y.H.1
Lou, Y.2
-
11
-
-
0000002470
-
Strips or spots? Nonlinear effects in bifurcation of reaction-diffusion equation on the square
-
Ermentrout B. Strips or spots? Nonlinear effects in bifurcation of reaction-diffusion equation on the square. Proc. R. Soc. Lond. 434 (1991) 413-417
-
(1991)
Proc. R. Soc. Lond.
, vol.434
, pp. 413-417
-
-
Ermentrout, B.1
-
15
-
-
55149099624
-
Turing pattern formation in the Brusselator model with superdiffusion
-
Golovin A.A., Matkowsky B.J., and Volpert V.A. Turing pattern formation in the Brusselator model with superdiffusion. SIAM J. Appl. Math. 69 (2009) 251-272
-
(2009)
SIAM J. Appl. Math.
, vol.69
, pp. 251-272
-
-
Golovin, A.A.1
Matkowsky, B.J.2
Volpert, V.A.3
-
16
-
-
41349095866
-
Modeling molecular interaction pathways using a two-stage identification algorithm
-
Gormley P., Li K., and Irwin G.W. Modeling molecular interaction pathways using a two-stage identification algorithm. Systems Synthetic Biol. 1 (2007) 145-160
-
(2007)
Systems Synthetic Biol.
, vol.1
, pp. 145-160
-
-
Gormley, P.1
Li, K.2
Irwin, G.W.3
-
17
-
-
0039978016
-
Geometric Theory of Semilinear Parabolic Equation
-
Springer-Verlag, Berlin
-
Henry D. Geometric Theory of Semilinear Parabolic Equation. Lecture Notes in Math. vol. 840 (1993), Springer-Verlag, Berlin
-
(1993)
Lecture Notes in Math.
, vol.840
-
-
Henry, D.1
-
18
-
-
0018305813
-
Multiple stable steady states and chemical hysteresis in a two-box model of the Brusselator
-
Jetschke G. Multiple stable steady states and chemical hysteresis in a two-box model of the Brusselator. J. Non-Equilib. Thermodyn. 4 2 (1979)
-
(1979)
J. Non-Equilib. Thermodyn.
, vol.4
, Issue.2
-
-
Jetschke, G.1
-
19
-
-
0030688319
-
Dynamical analysis of a reaction-diffusion system with Brusselator kinetics under feedback control
-
Albuquerque, NM, June
-
I. Karafyllis, P.D. Christofides, P. Daoutidis, Dynamical analysis of a reaction-diffusion system with Brusselator kinetics under feedback control, in: Proc. Amer. Control Conference, Albuquerque, NM, June 1997, pp. 2213-2217
-
(1997)
Proc. Amer. Control Conference
, pp. 2213-2217
-
-
Karafyllis, I.1
Christofides, P.D.2
Daoutidis, P.3
-
20
-
-
0034652878
-
Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion
-
Kan-on Y. Existence and instability of Neumann layer solutions for a 3-component Lotka-Volterra model with diffusion. J. Math. Anal. Appl. 243 (2000) 357-372
-
(2000)
J. Math. Anal. Appl.
, vol.243
, pp. 357-372
-
-
Kan-on, Y.1
-
21
-
-
0032389543
-
Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics
-
Kan-on Y., and Mimura M. Singular perturbation approach to a 3-component reaction-diffusion system arising in population dynamics. SIAM J. Math. Anal. 29 (1998) 1519-1536
-
(1998)
SIAM J. Math. Anal.
, vol.29
, pp. 1519-1536
-
-
Kan-on, Y.1
Mimura, M.2
-
22
-
-
0019197080
-
Two coupled neural oscillators as a model of the circadian pacemaker
-
Kawato M., and Suzuki R. Two coupled neural oscillators as a model of the circadian pacemaker. J. Theoret. Biol. 86 (1980) 547-575
-
(1980)
J. Theoret. Biol.
, vol.86
, pp. 547-575
-
-
Kawato, M.1
Suzuki, R.2
-
23
-
-
0036500993
-
Systems biology: a brief overview
-
Kitano H. Systems biology: a brief overview. Science 295 (2002) 1662-1664
-
(2002)
Science
, vol.295
, pp. 1662-1664
-
-
Kitano, H.1
-
24
-
-
0011958476
-
Period doubling bifurcations in a two-box model of the Brusselator
-
Klič. Period doubling bifurcations in a two-box model of the Brusselator. Aplikace Matematiky 28 (1983) 335-343
-
(1983)
Aplikace Matematiky
, vol.28
, pp. 335-343
-
-
Klič1
-
25
-
-
31144461544
-
Mesa-type patterns in one-dimensional Brusselator and their stability
-
Kolokolnikov T., Erneux T., and Wei J. Mesa-type patterns in one-dimensional Brusselator and their stability. Phys. D 214 1 (2006) 63-77
-
(2006)
Phys. D
, vol.214
, Issue.1
, pp. 63-77
-
-
Kolokolnikov, T.1
Erneux, T.2
Wei, J.3
-
26
-
-
18244407182
-
Spectral Theory and Nonlinear Functional Analysis
-
Chapman and Hall/CRC, Boca Raton, FL
-
López-Gómez J. Spectral Theory and Nonlinear Functional Analysis. Res. Notes Math. vol. 426 (2001), Chapman and Hall/CRC, Boca Raton, FL
-
(2001)
Res. Notes Math.
, vol.426
-
-
López-Gómez, J.1
-
27
-
-
55049131713
-
Algebraic Multiplicity of Eigenvalues of Linear Operators
-
Birkhäuser, Springer, Basel, Boston, Berlin
-
López-Gómez J., and Mora-Corral C. Algebraic Multiplicity of Eigenvalues of Linear Operators. Oper. Theory Adv. Appl. vol. 177 (2007), Birkhäuser, Springer, Basel, Boston, Berlin
-
(2007)
Oper. Theory Adv. Appl.
, vol.177
-
-
López-Gómez, J.1
Mora-Corral, C.2
-
28
-
-
0030579038
-
Diffusion, self-diffusion and cross-diffusion
-
Lou Y., and Ni W.M. Diffusion, self-diffusion and cross-diffusion. J. Differential Equations 131 (1996) 79-131
-
(1996)
J. Differential Equations
, vol.131
, pp. 79-131
-
-
Lou, Y.1
Ni, W.M.2
-
29
-
-
0033130048
-
Diffusion vs. cross-diffusion: an elliptic approach
-
Lou Y., and Ni W.M. Diffusion vs. cross-diffusion: an elliptic approach. J. Differential Equations 154 (1999) 157-190
-
(1999)
J. Differential Equations
, vol.154
, pp. 157-190
-
-
Lou, Y.1
Ni, W.M.2
-
30
-
-
0347055376
-
On 3 × 3 Lotka-Volterra competition systems with cross-diffusion
-
Lou Y., Martinez S., and Ni W.M. On 3 × 3 Lotka-Volterra competition systems with cross-diffusion. Discrete Contin. Dyn. Syst. 6 (2000) 175-190
-
(2000)
Discrete Contin. Dyn. Syst.
, vol.6
, pp. 175-190
-
-
Lou, Y.1
Martinez, S.2
Ni, W.M.3
-
31
-
-
1442279582
-
Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion
-
Pang P.Y.H., and Wang M.X. Non-constant positive steady states of a predator-prey system with non-monotonic functional response and diffusion. Proc. London Math. Soc. 88 (2004) 135-157
-
(2004)
Proc. London Math. Soc.
, vol.88
, pp. 135-157
-
-
Pang, P.Y.H.1
Wang, M.X.2
-
32
-
-
0141957171
-
Qualitative analysis of a ratio-dependent predator-prey system with diffusion
-
Pang P.Y.H., and Wang M.X. Qualitative analysis of a ratio-dependent predator-prey system with diffusion. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 919-942
-
(2003)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.133
, pp. 919-942
-
-
Pang, P.Y.H.1
Wang, M.X.2
-
33
-
-
0346340796
-
Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction
-
Peng R., and Wang M.X. Positive steady-state solutions of the Noyes-Field model for Belousov-Zhabotinskii reaction. Nonlinear Anal. 56 (2004) 451-464
-
(2004)
Nonlinear Anal.
, vol.56
, pp. 451-464
-
-
Peng, R.1
Wang, M.X.2
-
34
-
-
22144487744
-
Pattern formation in the Brusselator system
-
Peng R., and Wang M.X. Pattern formation in the Brusselator system. J. Math. Anal. Appl. 309 (2005) 151-166
-
(2005)
J. Math. Anal. Appl.
, vol.309
, pp. 151-166
-
-
Peng, R.1
Wang, M.X.2
-
35
-
-
36849102494
-
Symmetry-breaking instabilities in dissipative systems
-
Prigogine I., and Lefever R. Symmetry-breaking instabilities in dissipative systems. J. Chem. Phys. 48 (1968) 1665-1700
-
(1968)
J. Chem. Phys.
, vol.48
, pp. 1665-1700
-
-
Prigogine, I.1
Lefever, R.2
-
36
-
-
33846590412
-
The development of traveling waves in cubic auto-catalysis with different rates of diffusion
-
Qi Y. The development of traveling waves in cubic auto-catalysis with different rates of diffusion. Phys. D 226 (2007) 129-135
-
(2007)
Phys. D
, vol.226
, pp. 129-135
-
-
Qi, Y.1
-
37
-
-
49049139221
-
Strange attractors in coupled reaction-diffusion cells
-
Schreiber I., and Marek M. Strange attractors in coupled reaction-diffusion cells. Phys. D 5 (1982) 258-272
-
(1982)
Phys. D
, vol.5
, pp. 258-272
-
-
Schreiber, I.1
Marek, M.2
-
38
-
-
0002268213
-
Simple and complex reaction-diffusion fronts
-
Kapral R., and Showalter K. (Eds), Kluwer Acad. Publ., Dordrecht
-
Scott S.K., and Showalter K. Simple and complex reaction-diffusion fronts. In: Kapral R., and Showalter K. (Eds). Chemical Waves and Patterns (1995), Kluwer Acad. Publ., Dordrecht 485-516
-
(1995)
Chemical Waves and Patterns
, pp. 485-516
-
-
Scott, S.K.1
Showalter, K.2
-
39
-
-
0007393460
-
Transition to chaos via two-torus in coupled reaction-diffusion cells
-
Schreiber L., and Marek M. Transition to chaos via two-torus in coupled reaction-diffusion cells. Phys. Lett. 91 6 (1982) 263
-
(1982)
Phys. Lett.
, vol.91
, Issue.6
, pp. 263
-
-
Schreiber, L.1
Marek, M.2
-
41
-
-
0002011401
-
The chemical basis of morphogenesis
-
Turing A. The chemical basis of morphogenesis. Philos. Trans. R. Soc. Ser. B 237 (1952) 37-72
-
(1952)
Philos. Trans. R. Soc. Ser. B
, vol.237
, pp. 37-72
-
-
Turing, A.1
-
42
-
-
4244101701
-
Some further studies of nonlinear oscillations in chemical systems
-
Tyson J.J. Some further studies of nonlinear oscillations in chemical systems. J. Chem. Phys. 18 9 (1973)
-
(1973)
J. Chem. Phys.
, vol.18
, Issue.9
-
-
Tyson, J.J.1
-
44
-
-
0037845132
-
Non-constant positive steady-states of the Sel'kov model
-
Wang M.X. Non-constant positive steady-states of the Sel'kov model. J. Differential Equations 190 (2003) 600-620
-
(2003)
J. Differential Equations
, vol.190
, pp. 600-620
-
-
Wang, M.X.1
-
45
-
-
0035918674
-
A system of resource-based growth models with two resources in the unstirred chemostat
-
Wu J.H., and Wolkowicz G.S.K. A system of resource-based growth models with two resources in the unstirred chemostat. J. Differential Equations 172 (2001) 300-332
-
(2001)
J. Differential Equations
, vol.172
, pp. 300-332
-
-
Wu, J.H.1
Wolkowicz, G.S.K.2
-
46
-
-
3042513690
-
Stable squares and other oscillatory Turing patterns in a reaction-diffusion model
-
Yang L., Zhabotinsky A.M., and Epstein I.R. Stable squares and other oscillatory Turing patterns in a reaction-diffusion model. Phys. Rev. Lett. 92 198303 (2004) 1-4
-
(2004)
Phys. Rev. Lett.
, vol.92
, Issue.198303
, pp. 1-4
-
-
Yang, L.1
Zhabotinsky, A.M.2
Epstein, I.R.3
-
48
-
-
44949096501
-
Global dynamics of the Brusselator equations
-
You Y.C. Global dynamics of the Brusselator equations. Dyn. Partial Differ. Equ. 4 (2007) 167-196
-
(2007)
Dyn. Partial Differ. Equ.
, vol.4
, pp. 167-196
-
-
You, Y.C.1
|