Studies on the Existence of Unstable Oscillatory Patterns Bifurcating from Hopf Bifurcations in a Turing Model

المؤلفون المشاركون

Bao, Zhenhua
Zhang, Yan

المصدر

Journal of Applied Mathematics

العدد

المجلد 2014، العدد 2014 (31 ديسمبر/كانون الأول 2014)، ص ص. 1-5، 5ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2014-05-20

دولة النشر

مصر

عدد الصفحات

5

التخصصات الرئيسية

الرياضيات

الملخص 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.

نمط استشهاد جمعية علماء النفس الأمريكية (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

نمط استشهاد الجمعية الأمريكية للغات الحديثة (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

نمط استشهاد الجمعية الطبية الأمريكية (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

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-481992