-
1
-
-
0036141801
-
Mutual interference between predators can give rise to Turing spatial patterns
-
Alonso, D., Bartumeus, F., Catalan, J., 2002. Mutual interference between predators can give rise to Turing spatial patterns. Ecology 83(1), 28-34.
-
(2002)
Ecology
, vol.83
, Issue.1
, pp. 28-34
-
-
Alonso, D.1
Bartumeus, F.2
Catalan, J.3
-
2
-
-
0001737039
-
Implicit-explicit methods for time-dependent partial differential equations
-
Ascher, U., Ruuth, S., Wetton, B., 1995. Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32(3), 797-823.
-
(1995)
SIAM J. Numer. Anal
, vol.32
, Issue.3
, pp. 797-823
-
-
Ascher, U.1
Ruuth, S.2
Wetton, B.3
-
3
-
-
0035361441
-
On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution
-
Beckett, G., Mackenzie, J., 2001. On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution. J. Comput. Appl. Math. 131, 381-405.
-
(2001)
J. Comput. Appl. Math
, vol.131
, pp. 381-405
-
-
Beckett, G.1
Mackenzie, J.2
-
4
-
-
0003210742
-
The Mathematical Theory of Finite Element Methods
-
Springer, New York
-
Brenner, S., Scott, L., 1994. The Mathematical Theory of Finite Element Methods. Vol. 15: Texts in Applied Mathematics. Springer, New York.
-
(1994)
Texts in Applied Mathematics
, vol.15
-
-
Brenner, S.1
Scott, L.2
-
5
-
-
0040504616
-
The Finite Element Method for Elliptic Problems
-
North-Holland, Amsterdam
-
Ciarlet, P., 1979. The Finite Element Method for Elliptic Problems. Vol. 4: Studies in Mathematics and its Applications. North-Holland, Amsterdam.
-
(1979)
Studies in Mathematics and its Applications
, vol.4
-
-
Ciarlet, P.1
-
6
-
-
0027811215
-
The global dynamics of discrete semilinear parabolic equations
-
Elliott, C., Stuart, A., 1993. The global dynamics of discrete semilinear parabolic equations. SIAM J. Numer. Anal. 30(6), 1622-1663.
-
(1993)
SIAM J. Numer. Anal
, vol.30
, Issue.6
, pp. 1622-1663
-
-
Elliott, C.1
Stuart, A.2
-
7
-
-
0003809901
-
Deterministic Mathematical Models in Population Ecology
-
Marcel Dekker, New York
-
Freedman, H., 1980. Deterministic Mathematical Models in Population Ecology. Vol. 57: Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, New York.
-
(1980)
Monographs and Textbooks in Pure and Applied Mathematics
, vol.57
-
-
Freedman, H.1
-
8
-
-
58149255804
-
Analysis of two generic spatially extended predator-prey models
-
submitted for publication
-
Garvie, M., Trenchea, C., 2005a. Analysis of two generic spatially extended predator-prey models. Nonlinear Anal. Real World Appl., submitted for publication.
-
(2005)
Nonlinear Anal. Real World Appl
-
-
Garvie, M.1
Trenchea, C.2
-
9
-
-
33947538669
-
Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response
-
submitted for publication
-
Garvie, M., Trenchea, C., 2005b. Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response. Numer. Math., submitted for publication.
-
(2005)
Numer. Math
-
-
Garvie, M.1
Trenchea, C.2
-
10
-
-
0348077446
-
Functional responses for zooplankton feeding on multiple resources: A review of assumptions and biological dynamics
-
Gentleman, W., Leising, A., Frost, B., Strom, S., Murray, J., 2003. Functional responses for zooplankton feeding on multiple resources: A review of assumptions and biological dynamics. Deep Sea Res. II 50, 2847-2875.
-
(2003)
Deep Sea Res. II
, vol.50
, pp. 2847-2875
-
-
Gentleman, W.1
Leising, A.2
Frost, B.3
Strom, S.4
Murray, J.5
-
11
-
-
0031662774
-
Circles and spirals: Population persistence in a spatially explicit predator-prey model
-
Gurney, W., Veitch, A., Cruickshank, I., McGeachin, G., 1998. Circles and spirals: Population persistence in a spatially explicit predator-prey model. Ecology 79(7), 2516-2530.
-
(1998)
Ecology
, vol.79
, Issue.7
, pp. 2516-2530
-
-
Gurney, W.1
Veitch, A.2
Cruickshank, I.3
McGeachin, G.4
-
13
-
-
0000185875
-
Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations
-
Hoff, D., 1978. Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations. SIAM J. Numer. Anal. 15(6), 1161-1177.
-
(1978)
SIAM J. Numer. Anal
, vol.15
, Issue.6
, pp. 1161-1177
-
-
Hoff, D.1
-
14
-
-
84880026161
-
Some characteristics of simple types of predation and parasitism
-
Holling, C., 1959. Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, 385-398.
-
(1959)
Can. Entomol
, vol.91
, pp. 385-398
-
-
Holling, C.1
-
15
-
-
0002366911
-
The functional response of predators to prey density and its role in mimicry and population regulation
-
Holling, C., 1965. The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 45, 1-60.
-
(1965)
Mem. Entomol. Soc. Can
, vol.45
, pp. 1-60
-
-
Holling, C.1
-
16
-
-
0028176208
-
Partial differential equations in ecology: Spatial interactions and population dynamics
-
Holmes, E., Lewis, M., Banks, J., Veit, R., 1994. Partial differential equations in ecology: Spatial interactions and population dynamics. Ecology 75(1), 17-29.
-
(1994)
Ecology
, vol.75
, Issue.1
, pp. 17-29
-
-
Holmes, E.1
Lewis, M.2
Banks, J.3
Veit, R.4
-
19
-
-
0021553164
-
Fully discrete stability and invariant rectangular regions for reaction-diffusion systems
-
Jerome, J., 1984. Fully discrete stability and invariant rectangular regions for reaction-diffusion systems. SIAM J. Numer. Anal. 21(6), 1054-1065.
-
(1984)
SIAM J. Numer. Anal
, vol.21
, Issue.6
, pp. 1054-1065
-
-
Jerome, J.1
-
20
-
-
0036162215
-
Predator functional responses: Discriminating between handling and digesting prey
-
Jeschke, J., Kopp, M., Tollrian, R., 2002. Predator functional responses: Discriminating between handling and digesting prey. Ecol. Monogr. 72(1), 95-112.
-
(2002)
Ecol. Monogr
, vol.72
, Issue.1
, pp. 95-112
-
-
Jeschke, J.1
Kopp, M.2
Tollrian, R.3
-
21
-
-
0039291305
-
Convergence and stability analysis of an explicit finite difference method for 2-dimensional reaction-diffusion equations
-
Li, N., Steiner, J., Tang, S.-M., 1994. Convergence and stability analysis of an explicit finite difference method for 2-dimensional reaction-diffusion equations. J. Aust. Math. Soc. Ser. B 36(2), 234-241.
-
(1994)
J. Aust. Math. Soc. Ser. B
, vol.36
, Issue.2
, pp. 234-241
-
-
Li, N.1
Steiner, J.2
Tang, S.-M.3
-
22
-
-
0037119527
-
Dynamical stabilization of an unstable equilibrium in chemical and biological systems
-
Malchow, H., Petrovskii, S., 2002. Dynamical stabilization of an unstable equilibrium in chemical and biological systems. Math. Comput. Model. 36, 307-319.
-
(2002)
Math. Comput. Model
, vol.36
, pp. 307-319
-
-
Malchow, H.1
Petrovskii, S.2
-
24
-
-
0036733930
-
Spatiotemporal complexity of plankton and fish dynamics
-
Medvinsky, A., Petrovskii, S., Tikhonova, I., Malchow, H., Li, B.-L., 2002. Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44(3), 311-370.
-
(2002)
SIAM Rev
, vol.44
, Issue.3
, pp. 311-370
-
-
Medvinsky, A.1
Petrovskii, S.2
Tikhonova, I.3
Malchow, H.4
Li, B.-L.5
-
25
-
-
0037284570
-
A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion
-
Mickens, R., 2003. A nonstandard finite difference scheme for a Fisher PDE having nonlinear diffusion. Comput. Math. Appl. 45, 429-436.
-
(2003)
Comput. Math. Appl
, vol.45
, pp. 429-436
-
-
Mickens, R.1
-
27
-
-
0003363592
-
Mathematical Biology
-
Springer, Berlin
-
Murray, J., 1993. Mathematical Biology. Vol. 19: Biomathematics Texts. Springer, Berlin.
-
(1993)
Biomathematics Texts
, vol.19
-
-
Murray, J.1
-
28
-
-
0036161027
-
Transient dynamics and pattern formation: Reactivity is necessary for Turing instabilities
-
Neubert, M., Caswell, H., Murray, J., 2002. Transient dynamics and pattern formation: Reactivity is necessary for Turing instabilities. Math. Biosci. 175, 1-11.
-
(2002)
Math. Biosci
, vol.175
, pp. 1-11
-
-
Neubert, M.1
Caswell, H.2
Murray, J.3
-
29
-
-
0032391453
-
Accelerated monotone iterative methods for finite difference equations of reaction-diffusion
-
Pao, C., 1998. Accelerated monotone iterative methods for finite difference equations of reaction-diffusion. Numer. Math. 79, 261-281.
-
(1998)
Numer. Math
, vol.79
, pp. 261-281
-
-
Pao, C.1
-
30
-
-
0001326901
-
Numerical analysis of coupled systems of nonlinear parabolic equations
-
Pao, C., 1999. Numerical analysis of coupled systems of nonlinear parabolic equations. SIAM J. Numer. Anal. 36(2), 393-416.
-
(1999)
SIAM J. Numer. Anal
, vol.36
, Issue.2
, pp. 393-416
-
-
Pao, C.1
-
31
-
-
0037104634
-
Finite difference reaction-diffusion systems with coupled boundary conditions and time delays
-
Pao, C., 2002. Finite difference reaction-diffusion systems with coupled boundary conditions and time delays. J. Math. Anal. 272, 407-434.
-
(2002)
J. Math. Anal
, vol.272
, pp. 407-434
-
-
Pao, C.1
-
32
-
-
0027806283
-
Diffusion-induced chaos in a spatial predator-prey system
-
Pascual, M., 1993. Diffusion-induced chaos in a spatial predator-prey system. Proc. R. Soc. Lond. Ser. B 251, 1-7.
-
(1993)
Proc. R. Soc. Lond. Ser. B
, vol.251
, pp. 1-7
-
-
Pascual, M.1
-
33
-
-
0033120656
-
A minimal model of pattern formation in a prey-predator system
-
Petrovskii, S., Malchow, H., 1999. A minimal model of pattern formation in a prey-predator system. Math. Comput. Model. 29, 49-63.
-
(1999)
Math. Comput. Model
, vol.29
, pp. 49-63
-
-
Petrovskii, S.1
Malchow, H.2
-
34
-
-
0035718414
-
Wave of chaos: New mechanism of pattern formation in spatiotemporal population dynamics
-
Petrovskii, S., Malchow, H., 2001. Wave of chaos: New mechanism of pattern formation in spatiotemporal population dynamics. Theor. Populat. Biol. 59, 157-174.
-
(2001)
Theor. Populat. Biol
, vol.59
, pp. 157-174
-
-
Petrovskii, S.1
Malchow, H.2
-
36
-
-
0037608679
-
-
Pujol, M., Grimalt, P., 2002. A non-linear model for cerebral diffusion: Stability of finite differences method and resolution using the Adomian method. Int. J. Numer. Method H 13(4), 473-485.
-
Pujol, M., Grimalt, P., 2002. A non-linear model for cerebral diffusion: Stability of finite differences method and resolution using the Adomian method. Int. J. Numer. Method H 13(4), 473-485.
-
-
-
-
37
-
-
1642382839
-
Is diffusion-induced chaos robust?
-
Rai, V., Jayaraman, G., 2003. Is diffusion-induced chaos robust? Curr. Sci. India 84(7), 925-929.
-
(2003)
Curr. Sci. India
, vol.84
, Issue.7
, pp. 925-929
-
-
Rai, V.1
Jayaraman, G.2
-
39
-
-
0001524523
-
Graphical representation and stability conditions for predator-prey interaction
-
Rosenzweig, M., MacArthur, R., 1963. Graphical representation and stability conditions for predator-prey interaction. Am. Nat. 97, 209-223.
-
(1963)
Am. Nat
, vol.97
, pp. 209-223
-
-
Rosenzweig, M.1
MacArthur, R.2
-
40
-
-
0001248878
-
Implicit-explicit methods for reaction-diffusion problems in pattern formation
-
Ruuth, J., 1995. Implicit-explicit methods for reaction-diffusion problems in pattern formation. J. Math. Biol. 34, 148-176.
-
(1995)
J. Math. Biol
, vol.34
, pp. 148-176
-
-
Ruuth, J.1
-
42
-
-
0000048673
-
GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems
-
Saad, Y., Schultz, M., 1986. GMRES: A generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856-869.
-
(1986)
SIAM J. Sci. Stat. Comput
, vol.7
, Issue.3
, pp. 856-869
-
-
Saad, Y.1
Schultz, M.2
-
43
-
-
0033383624
-
Competition and dispersal in predator-prey waves
-
Savill, N., Hogeweg, P., 1999. Competition and dispersal in predator-prey waves. Theor. Populat. Biol. 56, 243-263.
-
(1999)
Theor. Populat. Biol
, vol.56
, pp. 243-263
-
-
Savill, N.1
Hogeweg, P.2
-
44
-
-
0015442349
-
Dissipative structure: An explanation and an ecological example
-
Segel, L., Jackson, J., 1972. Dissipative structure: An explanation and an ecological example. J. Theor. Biol. 37, 545-559.
-
(1972)
J. Theor. Biol
, vol.37
, pp. 545-559
-
-
Segel, L.1
Jackson, J.2
-
45
-
-
0035127918
-
Periodic travelling waves in cyclic predator-prey systems
-
Sherratt, J., 2001. Periodic travelling waves in cyclic predator-prey systems. Ecol. Lett. 4, 30-37.
-
(2001)
Ecol. Lett
, vol.4
, pp. 30-37
-
-
Sherratt, J.1
-
46
-
-
0030814768
-
Oscillations and chaos behind predator-prey invasion: Mathematical artifact or ecological reality?
-
Sherratt, J., Eagan, B., Lewis, M., 1997. Oscillations and chaos behind predator-prey invasion: Mathematical artifact or ecological reality? Phil. Trans. R. Soc. Lond. B 352, 21-38.
-
(1997)
Phil. Trans. R. Soc. Lond. B
, vol.352
, pp. 21-38
-
-
Sherratt, J.1
Eagan, B.2
Lewis, M.3
-
47
-
-
53149140283
-
Generation of periodic waves by landscape features in cyclic predator-prey systems
-
Sherratt, J., Lambin, X., Thomas, C., Sherratt, T., 2002. Generation of periodic waves by landscape features in cyclic predator-prey systems. Proc. R. Soc. Lond. Ser. B 269, 327-334.
-
(2002)
Proc. R. Soc. Lond. Ser. B
, vol.269
, pp. 327-334
-
-
Sherratt, J.1
Lambin, X.2
Thomas, C.3
Sherratt, T.4
-
48
-
-
0028921952
-
Ecological chaos in the wake of invasion
-
Sherratt, J., Lewis, M., Fowler, A., 1995. Ecological chaos in the wake of invasion. Proc. Natl. Acad. Sci. U.S.A. 92, 2524-2528.
-
(1995)
Proc. Natl. Acad. Sci. U.S.A
, vol.92
, pp. 2524-2528
-
-
Sherratt, J.1
Lewis, M.2
Fowler, A.3
-
49
-
-
0035658752
-
Functional responses with predator interference: Viable alternatives to the Holling type II model
-
Skalski, G., Gilliam, J.F., 2001. Functional responses with predator interference: Viable alternatives to the Holling type II model. Ecology 82(11), 3083-3092.
-
(2001)
Ecology
, vol.82
, Issue.11
, pp. 3083-3092
-
-
Skalski, G.1
Gilliam, J.F.2
-
50
-
-
0003233281
-
Shock Waves and Reaction-Diffusion Equations
-
Wissenschaften. Springer-Verlag, New York
-
Smoller, J., 1983. Shock Waves and Reaction-Diffusion Equations. Vol. 258: Grundlehren der mathematischen Wissenschaften. Springer-Verlag, New York.
-
(1983)
Grundlehren der mathematischen
, vol.258
-
-
Smoller, J.1
-
51
-
-
0024682304
-
Nonlinear instability in dissipative finite difference schemes
-
Stuart, A., 1989. Nonlinear instability in dissipative finite difference schemes. SIAM Rev. 31(2), 191-220.
-
(1989)
SIAM Rev
, vol.31
, Issue.2
, pp. 191-220
-
-
Stuart, A.1
-
53
-
-
0002011401
-
The chemical basis of morphogenesis
-
Turing, A., 1952. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37-72.
-
(1952)
Phil. Trans. R. Soc. Lond. B
, vol.237
, pp. 37-72
-
-
Turing, A.1
-
54
-
-
0344375578
-
Global asymptotic behavior of iterative implicit schemes
-
Yee, H., Sweby, P., 1994. Global asymptotic behavior of iterative implicit schemes. Int. J. Bifurcat. Chaos 4(6), 1579-1611.
-
(1994)
Int. J. Bifurcat. Chaos
, vol.4
, Issue.6
, pp. 1579-1611
-
-
Yee, H.1
Sweby, P.2
-
55
-
-
84954811121
-
Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations II. Global asymptotic behaviour of time discretizations
-
Yee, H., Sweby, P., 1995. Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations II. Global asymptotic behaviour of time discretizations. Comp. Fluid Dyn. 4, 219-283.
-
(1995)
Comp. Fluid Dyn
, vol.4
, pp. 219-283
-
-
Yee, H.1
Sweby, P.2
|