الملخص
A zero-Hopf equilibrium in a three-dimensional system is an isolated equilibrium point which has a zero eigenvalue and a simple pair of purely imaginary eigenvalues. In general, for such an equilibrium, there is no theory for finding when some periodic solutions are bifurcated by perturbing the parameters of the system. In this work, we describe the values of the parameters for which a zero-Hopf equilibrium occurs at the equilibrium points in the generalized stretch-twist-fold flow. Thus, only one condition for parameters of the generalized stretch-twist-fold flow introduced in a system (Eq. 1) is found for which the equilibrium point is a zero-Hopf equilibrium. For this condition, we use the averaging method to provide the existence of a periodic solution, which bifurcates from the zero-Hopf equilibrium point. The main result in this paper is Theorem 1, which gives a periodic solution of the generalized stretch-twist-fold flow.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.24200/squjs.vol24iss2pp122-128
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 24(2), 122
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY 4.0
اقتبس هذه المقالة
APA 7
Hussein, N. H., & Amen, A. I. (2020). Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow. Sultan Qaboos University Journal for Science, 24(2), 122. https://doi.org/10.24200/squjs.vol24iss2pp122-128
MLA 9
Hussein, Niazy Hady, and Azad Ibrahim Amen. "Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow." Sultan Qaboos University Journal for Science, vol. 24, no. 2, 2020, pp. 122. https://doi.org/10.24200/squjs.vol24iss2pp122-128.
شيكاغو (المؤلف–التاريخ)
Hussein, Niazy Hady, and Azad Ibrahim Amen. 2020. "Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow." Sultan Qaboos University Journal for Science 24 (2): 122. https://doi.org/10.24200/squjs.vol24iss2pp122-128.
هارفارد
Hussein, N. H. and Amen, A. I. (2020) 'Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow', Sultan Qaboos University Journal for Science, 24(2), pp. 122. doi:10.24200/squjs.vol24iss2pp122-128.
فانكوفر
Hussein NH, Amen AI. Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow. Sultan Qaboos University Journal for Science. 2020;24(2):122. doi:10.24200/squjs.vol24iss2pp122-128
IEEE
N. H. Hussein, and A. I. Amen, "Zero-Hopf Bifurcation in the Generalized Stretch-Twist-Fold Flow," Sultan Qaboos University Journal for Science, vol. 24, no. 2, pp. 122, 2020, doi: 10.24200/squjs.vol24iss2pp122-128.