-
1
-
-
0001339498
-
Global bifurcation of positive solutions in some systems of elliptic equations
-
Blat J., and Brown K.J. Global bifurcation of positive solutions in some systems of elliptic equations. SIAM J. Math. Anal. 17 (1986) 1339-1353
-
(1986)
SIAM J. Math. Anal.
, vol.17
, pp. 1339-1353
-
-
Blat, J.1
Brown, K.J.2
-
3
-
-
0018737036
-
Convergence to homogeneous equilibrium state for generalized Volterra-Lotka systems with diffusion
-
De Mottoni P., and Rothe F. Convergence to homogeneous equilibrium state for generalized Volterra-Lotka systems with diffusion. SIAM J. Appl. Math. 37 (1979) 648-663
-
(1979)
SIAM J. Appl. Math.
, vol.37
, pp. 648-663
-
-
De Mottoni, P.1
Rothe, F.2
-
4
-
-
0001674774
-
S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model
-
Du Y.H., and Lou Y. S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model. J. Differential Equations 144 (1998) 390-440
-
(1998)
J. Differential Equations
, vol.144
, pp. 390-440
-
-
Du, Y.H.1
Lou, Y.2
-
5
-
-
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
-
6
-
-
36148989064
-
Some recent results on diffusive predator-prey models in spatially heterogeneous environment
-
Nonlinear Dynamics and Evolution Equations, Amer. Math. Soc., Providence, RI
-
Du Y.H., and Shi J.P. Some recent results on diffusive predator-prey models in spatially heterogeneous environment. Nonlinear Dynamics and Evolution Equations. Fields Inst. Commun. vol. 48 (2006), Amer. Math. Soc., Providence, RI 95-135
-
(2006)
Fields Inst. Commun.
, vol.48
, pp. 95-135
-
-
Du, Y.H.1
Shi, J.P.2
-
7
-
-
36148940895
-
Allee effect and bistability in a spatially heterogeneous predator-prey model
-
Du Y.H., and Shi J.P. Allee effect and bistability in a spatially heterogeneous predator-prey model. Trans. Amer. Math. Soc. 359 (2007) 4557-4593
-
(2007)
Trans. Amer. Math. Soc.
, vol.359
, pp. 4557-4593
-
-
Du, Y.H.1
Shi, J.P.2
-
8
-
-
0041625080
-
Elliptic Partial Differential Equation of Second Order
-
Springer-Verlag, Berlin Reprint of the 1998 edition
-
Gilbarg D., and Trudinger N.S. Elliptic Partial Differential Equation of Second Order. Classics Math. (2001), Springer-Verlag, Berlin Reprint of the 1998 edition
-
(2001)
Classics Math.
-
-
Gilbarg, D.1
Trudinger, N.S.2
-
9
-
-
0018194555
-
Global stability of two-species systems
-
Hastings A. Global stability of two-species systems. J. Math. Biol. 5 (1977) 399-403
-
(1977)
J. Math. Biol.
, vol.5
, pp. 399-403
-
-
Hastings, A.1
-
10
-
-
0003304963
-
Geometric Theory of Semilinear Parabolic Equations
-
Springer-Verlag, Berlin, New York
-
Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. vol. 840 (1981), Springer-Verlag, Berlin, New York
-
(1981)
Lecture Notes in Math.
, vol.840
-
-
Henry, D.1
-
11
-
-
84880026161
-
Some characteristics of simple types of predation and parasitism
-
Holling C.S. Some characteristics of simple types of predation and parasitism. Canad. Entomologist 91 (1959) 385-398
-
(1959)
Canad. Entomologist
, vol.91
, pp. 385-398
-
-
Holling, C.S.1
-
12
-
-
67349127318
-
Relaxation oscillator profile of limit cycle in predator-prey system
-
doi:10.3934/dcdsb.2009.11.xx
-
S.B. Hsu, J.P. Shi, Relaxation oscillator profile of limit cycle in predator-prey system, Discrete Contin. Dyn. Syst. Ser. B, doi:10.3934/dcdsb.2009.11.xx
-
Discrete Contin. Dyn. Syst. Ser. B
-
-
Hsu, S.B.1
Shi, J.P.2
-
13
-
-
0000809487
-
Experimental studies on predation: Dispersion factors and predator-prey oscillations
-
Huffaker C.B. Experimental studies on predation: Dispersion factors and predator-prey oscillations. Hilgardia 27 (1958) 343-383
-
(1958)
Hilgardia
, vol.27
, pp. 343-383
-
-
Huffaker, C.B.1
-
14
-
-
26444528184
-
Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model
-
Jang J., Ni W.M., and Tang M.X. Global bifurcation and structure of Turing patterns in the 1-D Lengyel-Epstein model. J. Dynam. Differential Equations 16 (2004) 297-320
-
(2004)
J. Dynam. Differential Equations
, vol.16
, pp. 297-320
-
-
Jang, J.1
Ni, W.M.2
Tang, M.X.3
-
15
-
-
67349115753
-
Bifurcations of patterned solutions in diffusive Lengyel-Epstein system of CIMA chemical reaction
-
submitted for publication
-
J.Y. Jin, J.P. Shi, J.J. Wei, F.Q. Yi, Bifurcations of patterned solutions in diffusive Lengyel-Epstein system of CIMA chemical reaction, submitted for publication
-
-
-
Jin, J.Y.1
Shi, J.P.2
Wei, J.J.3
Yi, F.Q.4
-
16
-
-
0023469857
-
Habitat fragmentation and the stability of predator-prey interactions
-
Kareiva P. Habitat fragmentation and the stability of predator-prey interactions. Nature 326 (1987) 388-390
-
(1987)
Nature
, vol.326
, pp. 388-390
-
-
Kareiva, P.1
-
17
-
-
0023504111
-
Swarms of predators exhibit "preytaxis" if individual predators use area-restricted search
-
Kareiva P., and Odell G. Swarms of predators exhibit "preytaxis" if individual predators use area-restricted search. Amer. Natur. 130 (1987) 233-270
-
(1987)
Amer. Natur.
, vol.130
, pp. 233-270
-
-
Kareiva, P.1
Odell, G.2
-
18
-
-
33749640702
-
Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge
-
Ko W., and Ryu K. Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge. J. Differential Equations 231 (2006) 534-550
-
(2006)
J. Differential Equations
, vol.231
, pp. 534-550
-
-
Ko, W.1
Ryu, K.2
-
19
-
-
0017852514
-
Limiting behaviour for a prey-predator model with diffusion and crowding effects
-
Leung A. Limiting behaviour for a prey-predator model with diffusion and crowding effects. J. Math. Biol. 6 (1978) 87-93
-
(1978)
J. Math. Biol.
, vol.6
, pp. 87-93
-
-
Leung, A.1
-
20
-
-
36849153282
-
An hypothesis for the origin of planktonic patchiness
-
Levin S.A., and Segel L.A. An hypothesis for the origin of planktonic patchiness. Nature 259 (1976) 659
-
(1976)
Nature
, vol.259
, pp. 659
-
-
Levin, S.A.1
Segel, L.A.2
-
21
-
-
25144497411
-
Bounds for the steady-state Sel'kov model for arbitrary p in any number of dimensions
-
Lieberman G.M. Bounds for the steady-state Sel'kov model for arbitrary p in any number of dimensions. SIAM J. Math. Anal. 36 (2005) 1400-1406
-
(2005)
SIAM J. Math. Anal.
, vol.36
, pp. 1400-1406
-
-
Lieberman, G.M.1
-
22
-
-
0002542873
-
Large amplitude stationary solutions to a chemotaxis systems
-
Lin C.S., Ni W.M., and Takagi I. Large amplitude stationary solutions to a chemotaxis systems. J. Differential Equations 72 (1988) 1-27
-
(1988)
J. Differential Equations
, vol.72
, pp. 1-27
-
-
Lin, C.S.1
Ni, W.M.2
Takagi, I.3
-
23
-
-
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
-
24
-
-
0036733930
-
Spatiotemporal complexity of plankton and fish dynamics
-
Medvinsky A.B., Petrovskii S.V., Tikhonova I.A., Malchow H., and Li B.-L. Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 44 (2002) 311-370
-
(2002)
SIAM Rev.
, vol.44
, pp. 311-370
-
-
Medvinsky, A.B.1
Petrovskii, S.V.2
Tikhonova, I.A.3
Malchow, H.4
Li, B.-L.5
-
25
-
-
0018224543
-
On a diffusive prey-predator model which exhibits patchiness
-
Mimura M., and Murray J.D. On a diffusive prey-predator model which exhibits patchiness. J. Theoret. Biol. 75 (1978) 249-262
-
(1978)
J. Theoret. Biol.
, vol.75
, pp. 249-262
-
-
Mimura, M.1
Murray, J.D.2
-
27
-
-
0346582863
-
Mathematical Biology. I. An Introduction
-
Springer-Verlag, New York II. Spatial Models and Biomedical Applications
-
Murray J.D. Mathematical Biology. I. An Introduction. Interdiscip. Appl. Math. vol. 17 (2002), Springer-Verlag, New York II. Spatial Models and Biomedical Applications
-
(2002)
Interdiscip. Appl. Math.
, vol.17
-
-
Murray, J.D.1
-
28
-
-
0346582863
-
Mathematical Biology. I. An Introduction
-
Springer-Verlag, New York
-
Murray J.D. Mathematical Biology. I. An Introduction. Interdiscip. Appl. Math. vol. 18 (2002), Springer-Verlag, New York
-
(2002)
Interdiscip. Appl. Math.
, vol.18
-
-
Murray, J.D.1
-
29
-
-
0001347301
-
Global structure of bifurcating solutions of some reaction-diffusion systems
-
Nishiura Y. Global structure of bifurcating solutions of some reaction-diffusion systems. SIAM J. Math. Anal. 13 (1982) 555-593
-
(1982)
SIAM J. Math. Anal.
, vol.13
, pp. 555-593
-
-
Nishiura, Y.1
-
30
-
-
1342300494
-
Diffusion and Ecological Problems: Modern Perspectives
-
Springer-Verlag, New York
-
Okubo A., and Levin S. Diffusion and Ecological Problems: Modern Perspectives. Interdiscip. Appl. Math. second ed. vol. 14 (2001), Springer-Verlag, New York
-
(2001)
Interdiscip. Appl. Math. second ed.
, vol.14
-
-
Okubo, A.1
Levin, S.2
-
31
-
-
34548394552
-
Qualitative analysis of steady states to the Sel'kov model
-
Peng R. Qualitative analysis of steady states to the Sel'kov model. J. Differential Equations 241 (2007) 386-398
-
(2007)
J. Differential Equations
, vol.241
, pp. 386-398
-
-
Peng, R.1
-
32
-
-
35348966287
-
Stationary pattern of a ratio-dependent food chain model with diffusion
-
Peng R., Shi J.P., and Wang M.X. Stationary pattern of a ratio-dependent food chain model with diffusion. SIAM J. Appl. Math. 67 (2007) 1479-1503
-
(2007)
SIAM J. Appl. Math.
, vol.67
, pp. 1479-1503
-
-
Peng, R.1
Shi, J.P.2
Wang, M.X.3
-
33
-
-
44949117505
-
On stationary patterns of a reaction-diffusion model with autocatalysis and saturation law
-
Peng R., Shi J.P., and Wang M.X. On stationary patterns of a reaction-diffusion model with autocatalysis and saturation law. Nonlinearity 21 (2008) 1471-1488
-
(2008)
Nonlinearity
, vol.21
, pp. 1471-1488
-
-
Peng, R.1
Shi, J.P.2
Wang, M.X.3
-
34
-
-
14644406942
-
Positive steady-states of the Holling-Tanner prey-predator model with diffusion
-
Peng R., and Wang M.X. Positive steady-states of the Holling-Tanner prey-predator model with diffusion. Proc. Roy. Soc. Edinburgh Sect. A 135 16 (2005) 149-164
-
(2005)
Proc. Roy. Soc. Edinburgh Sect. A
, vol.135
, Issue.16
, pp. 149-164
-
-
Peng, R.1
Wang, M.X.2
-
35
-
-
36448974335
-
Some global results for nonlinear eigenvalue problems
-
Rabinowitz P.H. Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7 (1971) 487-513
-
(1971)
J. Funct. Anal.
, vol.7
, pp. 487-513
-
-
Rabinowitz, P.H.1
-
36
-
-
0001524523
-
Graphical representation and stability conditions of predator-prey interactions
-
Rosenzweig M.L., and MacArthur R. Graphical representation and stability conditions of predator-prey interactions. Amer. Natur. 97 (1963) 209-223
-
(1963)
Amer. Natur.
, vol.97
, pp. 209-223
-
-
Rosenzweig, M.L.1
MacArthur, R.2
-
37
-
-
0017151487
-
Convergence to the equilibrium state in the Volterra-Lotka diffusion equations
-
Rothe F. Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J. Math. Biol. 3 (1976) 319-324
-
(1976)
J. Math. Biol.
, vol.3
, pp. 319-324
-
-
Rothe, F.1
-
39
-
-
60349102594
-
On global bifurcation for quasilinear elliptic systems on bounded domains
-
Shi J.P., and Wang X.F. On global bifurcation for quasilinear elliptic systems on bounded domains. J. Differential Equations 246 (2009) 2788-2812
-
(2009)
J. Differential Equations
, vol.246
, pp. 2788-2812
-
-
Shi, J.P.1
Wang, X.F.2
-
40
-
-
38949167125
-
Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
-
Yi F.Q., Wei J.J., and Shi J.P. Diffusion-driven instability and bifurcation in the Lengyel-Epstein system. Nonlinear Anal. Real World Appl. 9 (2008) 1038-1051
-
(2008)
Nonlinear Anal. Real World Appl.
, vol.9
, pp. 1038-1051
-
-
Yi, F.Q.1
Wei, J.J.2
Shi, J.P.3
-
41
-
-
55649115788
-
Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system
-
Yi F.Q., Wei J.J., and Shi J.P. Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system. Appl. Math. Lett. 22 (2009) 52-55
-
(2009)
Appl. Math. Lett.
, vol.22
, pp. 52-55
-
-
Yi, F.Q.1
Wei, J.J.2
Shi, J.P.3
-
42
-
-
58749112528
-
Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
-
Yi F.Q., Wei J.J., and Shi J.P. Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system. J. Differential Equations 246 (2009) 1944-1977
-
(2009)
J. Differential Equations
, vol.246
, pp. 1944-1977
-
-
Yi, F.Q.1
Wei, J.J.2
Shi, J.P.3
|