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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.
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참고문헌 (9)
참고문헌 신청
A. M. Turing / 1952 / The chemical basis of morphogenesis / Philos. Trans. Roy. Soc. London Ser. B 237 (641) : 37 ~ 72
B. D. Hassard / 1981 / Theory and Applications of Hopf Bifurcation / Cambridge University Press
F. Yi / 2008 / Diffusion-driven instability and bifurcation in the Lengyel-Epstein system / Nonlinear Anal. Real World Appl 9 (3) : 1038 ~ 1051
F. Yi / 2009 / Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system / J. Differential Equations 246 (5) : 1944 ~ 1977
H. Degn / 1969 / Theory of oscillations of respiration rate in continuous culture of klebsiella aerogenes / J. Theoret. Biol 22 (22) : 238 ~ 248
B. D. Hassard / 1981 / Theory and Applications of Hopf Bifurcation / Cambridge University Press
F. Yi / 2008 / Diffusion-driven instability and bifurcation in the Lengyel-Epstein system / Nonlinear Anal. Real World Appl 9 (3) : 1038 ~ 1051
F. Yi / 2009 / Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system / J. Differential Equations 246 (5) : 1944 ~ 1977
H. Degn / 1969 / Theory of oscillations of respiration rate in continuous culture of klebsiella aerogenes / J. Theoret. Biol 22 (22) : 238 ~ 248
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