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Oscillations of many interfaces in the near-shadow regime of two-component reaction-diffusion systems
1. | Dalhousie University, Halifax, NS, Canada, Canada |
References:
[1] |
M. Banerjee and S. Petrovski, Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system, Theor Ecol, 4 (2011), 37-53.
doi: 10.1007/s12080-010-0073-1. |
[2] |
W. Chen and M. J. Ward, Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional gray-scott model, European Journal of Applied Mathematics, 20 (2009), 187-214.
doi: 10.1017/S0956792508007766. |
[3] |
S. Ei, H. Ikeda and T. Kawana, Dynamics of front solutions in a specific reaction-diffusion system in one dimension, Japan J. Indust. Appl. Math., 25 (2008), 117-147.
doi: 10.1007/BF03167516. |
[4] |
S. Gurevich, S. Amiranashvili and H.-G. Purwins, Breathing dissipative solitons in three-component reaction-diffusion system, Physical Review E, 74 (2006), 066201, 7pp.
doi: 10.1103/PhysRevE.74.066201. |
[5] |
A. Hagberg and E. Meron, Pattern formation in non-gradient reaction-diffusion systems: the effect of front bifurcations, Nonlinearity, 7 (1994), 805-835.
doi: 10.1088/0951-7715/7/3/006. |
[6] |
D. Haim, G. Li, Q. Ouyang, W. D. McCormick, H. L. Swinney, A. Hagberg and E. Meron, Breathing spots in a reaction-diffusion system, Physical review letters, 77 (1996), p190. |
[7] |
H. Hardway and Y.-X. Li, Stationary and oscillatory fronts in a two-component genetic regulatory network model, Physica D, 239 (2010), 1650-1661.
doi: 10.1016/j.physd.2010.04.009. |
[8] |
H. Ikeda and T. Ikeda, Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems, Journal of Dynamics and Differential Equations, 12 (2000), 117-167.
doi: 10.1023/A:1009098719440. |
[9] |
T. Ikeda and M. Mimura, An interfacial approach to regional segregation of two competing species mediated by a predator, Journal of Mathematical Biology, 31 (1993), 215-240.
doi: 10.1007/BF00166143. |
[10] |
T. Ikeda and Y. Nishiura, Pattern selection for two breathers, SIAM Journal on Applied Mathematics, 54 (1994), 195-230.
doi: 10.1137/S0036139992237250. |
[11] |
A. Kaminaga, V. K. Vanag and I. R. Epstein, A reaction-diffusion memory device, Angewandte Chemie International Edition, 45 (2006), 3087-3089. |
[12] |
S. Koga and Y. Kuramoto, Localized patterns in reaction-diffusion systems, Progress of Theoretical Physics, 63 (1980), 106-121.
doi: 10.1143/PTP.63.106. |
[13] |
T. Kolokolnikov and M. Tlidi, Spot deformation and replication in the two-dimensional belousov-zhabotinski reaction in a water-in-oil microemulsion, Physical review letters, 98 (2007), 188303.
doi: 10.1103/PhysRevLett.98.188303. |
[14] |
I. Lengyel and I. Epstein, Modeling of turing structures in the chlorite-iodide-malonic acid-starch reaction system, Science, 251 (1991), 650-652.
doi: 10.1126/science.251.4994.650. |
[15] |
Y.-X. Li, Tango waves in a bidomain model of fertilization calcium waves, Physica D, 186 (2003), 27-49.
doi: 10.1016/S0167-2789(03)00237-9. |
[16] |
R. McKay, T. Kolokolnikov and P. Muir, Interface oscillations in reaction-diffusion systems above the hopf bifurcation, Discrete and Continuous Dynamical Systems. Series BA Journal Bridging Mathematics and Sciences. |
[17] |
E. Meron, H. Yizhaq and E. Gilad, Localized structures in dryland vegetation: forms and functions, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17 (2007), 037109.
doi: 10.1063/1.2767246. |
[18] |
C. Muratov and V. V. Osipov, General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems, Phys, Rev. E, 53 (1996), 3101-3116.
doi: 10.1103/PhysRevE.53.3101. |
[19] |
M. Nagayama, K.-i. Ueda and M. Yadome, Numerical approach to transient dynamics of oscillatory pulses in a bistable reaction-diffusion system, Japan journal of industrial and applied mathematics, 27 (2010), 295-322.
doi: 10.1007/s13160-010-0015-8. |
[20] |
Y. Nishiura and M. Mimura, Layer oscillations in reaction-diffusion systems, SIAM J.Appl. Math, 49 (1989), 481-514.
doi: 10.1137/0149029. |
[21] |
T. Ohta, A. Ito and A. Tetsuka, Self-organization in an excitable reaction-diffusion system: synchronization of oscillatory domains in one dimension, Physical Review A, 42 (1990), 3225.
doi: 10.1103/PhysRevA.42.3225. |
[22] |
M. Suzuki, T. Ohta, M. Mimura and H. Sakaguchi, Breathing and wiggling motions in three-species laterally inhibitory systems, Physical Review E, 52 (1995), 3645-3655.
doi: 10.1103/PhysRevE.52.3645. |
[23] |
P. van Heijster, A. Doelman and T. J. Kaper, Pulse dynamics in a three-component system: Stability and bifurcations, Physica D, 237 (2008), 3335-3368.
doi: 10.1016/j.physd.2008.07.014. |
[24] |
V. K. Vanag and I. R. Epstein, Localized patterns in reaction-diffusion systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17 (2007), 037110, 11pp.
doi: 10.1063/1.2752494. |
[25] |
V. Volpert and S. Petrovskii, Reaction-diffusion waves in biology, Physics of Life Reviews, 6 (2009), 267-310.
doi: 10.1016/j.plrev.2009.10.002. |
[26] |
M. J. Ward and J. Wei, Hopf bifurcation and oscillatory instabilities of spike solutions for the one-dimensional gierer-meinhardt model, J. Nonlinear Science, 13 (2003), 209-264.
doi: 10.1007/s00332-002-0531-z. |
show all references
References:
[1] |
M. Banerjee and S. Petrovski, Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system, Theor Ecol, 4 (2011), 37-53.
doi: 10.1007/s12080-010-0073-1. |
[2] |
W. Chen and M. J. Ward, Oscillatory instabilities and dynamics of multi-spike patterns for the one-dimensional gray-scott model, European Journal of Applied Mathematics, 20 (2009), 187-214.
doi: 10.1017/S0956792508007766. |
[3] |
S. Ei, H. Ikeda and T. Kawana, Dynamics of front solutions in a specific reaction-diffusion system in one dimension, Japan J. Indust. Appl. Math., 25 (2008), 117-147.
doi: 10.1007/BF03167516. |
[4] |
S. Gurevich, S. Amiranashvili and H.-G. Purwins, Breathing dissipative solitons in three-component reaction-diffusion system, Physical Review E, 74 (2006), 066201, 7pp.
doi: 10.1103/PhysRevE.74.066201. |
[5] |
A. Hagberg and E. Meron, Pattern formation in non-gradient reaction-diffusion systems: the effect of front bifurcations, Nonlinearity, 7 (1994), 805-835.
doi: 10.1088/0951-7715/7/3/006. |
[6] |
D. Haim, G. Li, Q. Ouyang, W. D. McCormick, H. L. Swinney, A. Hagberg and E. Meron, Breathing spots in a reaction-diffusion system, Physical review letters, 77 (1996), p190. |
[7] |
H. Hardway and Y.-X. Li, Stationary and oscillatory fronts in a two-component genetic regulatory network model, Physica D, 239 (2010), 1650-1661.
doi: 10.1016/j.physd.2010.04.009. |
[8] |
H. Ikeda and T. Ikeda, Bifurcation phenomena from standing pulse solutions in some reaction-diffusion systems, Journal of Dynamics and Differential Equations, 12 (2000), 117-167.
doi: 10.1023/A:1009098719440. |
[9] |
T. Ikeda and M. Mimura, An interfacial approach to regional segregation of two competing species mediated by a predator, Journal of Mathematical Biology, 31 (1993), 215-240.
doi: 10.1007/BF00166143. |
[10] |
T. Ikeda and Y. Nishiura, Pattern selection for two breathers, SIAM Journal on Applied Mathematics, 54 (1994), 195-230.
doi: 10.1137/S0036139992237250. |
[11] |
A. Kaminaga, V. K. Vanag and I. R. Epstein, A reaction-diffusion memory device, Angewandte Chemie International Edition, 45 (2006), 3087-3089. |
[12] |
S. Koga and Y. Kuramoto, Localized patterns in reaction-diffusion systems, Progress of Theoretical Physics, 63 (1980), 106-121.
doi: 10.1143/PTP.63.106. |
[13] |
T. Kolokolnikov and M. Tlidi, Spot deformation and replication in the two-dimensional belousov-zhabotinski reaction in a water-in-oil microemulsion, Physical review letters, 98 (2007), 188303.
doi: 10.1103/PhysRevLett.98.188303. |
[14] |
I. Lengyel and I. Epstein, Modeling of turing structures in the chlorite-iodide-malonic acid-starch reaction system, Science, 251 (1991), 650-652.
doi: 10.1126/science.251.4994.650. |
[15] |
Y.-X. Li, Tango waves in a bidomain model of fertilization calcium waves, Physica D, 186 (2003), 27-49.
doi: 10.1016/S0167-2789(03)00237-9. |
[16] |
R. McKay, T. Kolokolnikov and P. Muir, Interface oscillations in reaction-diffusion systems above the hopf bifurcation, Discrete and Continuous Dynamical Systems. Series BA Journal Bridging Mathematics and Sciences. |
[17] |
E. Meron, H. Yizhaq and E. Gilad, Localized structures in dryland vegetation: forms and functions, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17 (2007), 037109.
doi: 10.1063/1.2767246. |
[18] |
C. Muratov and V. V. Osipov, General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems, Phys, Rev. E, 53 (1996), 3101-3116.
doi: 10.1103/PhysRevE.53.3101. |
[19] |
M. Nagayama, K.-i. Ueda and M. Yadome, Numerical approach to transient dynamics of oscillatory pulses in a bistable reaction-diffusion system, Japan journal of industrial and applied mathematics, 27 (2010), 295-322.
doi: 10.1007/s13160-010-0015-8. |
[20] |
Y. Nishiura and M. Mimura, Layer oscillations in reaction-diffusion systems, SIAM J.Appl. Math, 49 (1989), 481-514.
doi: 10.1137/0149029. |
[21] |
T. Ohta, A. Ito and A. Tetsuka, Self-organization in an excitable reaction-diffusion system: synchronization of oscillatory domains in one dimension, Physical Review A, 42 (1990), 3225.
doi: 10.1103/PhysRevA.42.3225. |
[22] |
M. Suzuki, T. Ohta, M. Mimura and H. Sakaguchi, Breathing and wiggling motions in three-species laterally inhibitory systems, Physical Review E, 52 (1995), 3645-3655.
doi: 10.1103/PhysRevE.52.3645. |
[23] |
P. van Heijster, A. Doelman and T. J. Kaper, Pulse dynamics in a three-component system: Stability and bifurcations, Physica D, 237 (2008), 3335-3368.
doi: 10.1016/j.physd.2008.07.014. |
[24] |
V. K. Vanag and I. R. Epstein, Localized patterns in reaction-diffusion systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17 (2007), 037110, 11pp.
doi: 10.1063/1.2752494. |
[25] |
V. Volpert and S. Petrovskii, Reaction-diffusion waves in biology, Physics of Life Reviews, 6 (2009), 267-310.
doi: 10.1016/j.plrev.2009.10.002. |
[26] |
M. J. Ward and J. Wei, Hopf bifurcation and oscillatory instabilities of spike solutions for the one-dimensional gierer-meinhardt model, J. Nonlinear Science, 13 (2003), 209-264.
doi: 10.1007/s00332-002-0531-z. |
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