Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-20
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain.
With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of proving the existence of Hopf bifurcations, which suggests the existence of spatially homogeneous and nonhomogeneous periodic solutions of this particular system.
In particular, we also prove that the spatial homogeneous periodic solutions bifurcating from the smallest Hopf bifurcation point of the system are always unstable.
This together with the instability results of the spatially nonhomogeneous periodic solutions by Yi et al., 2009, indicates that, in this model, all the oscillatory patterns from Hopf bifurcations are unstable.
American Psychological Association (APA)
Zhang, Yan& Bao, Zhenhua. 2014. Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-481992
Modern Language Association (MLA)
Zhang, Yan& Bao, Zhenhua. Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model. Journal of Applied Mathematics No. 2014 (2014), pp.1-5.
https://search.emarefa.net/detail/BIM-481992
American Medical Association (AMA)
Zhang, Yan& Bao, Zhenhua. Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-5.
https://search.emarefa.net/detail/BIM-481992
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-481992