首页 | 本学科首页   官方微博 | 高级检索  
     


Stability and bifurcation in a harmonic oscillator with delays
Affiliation:1. Automation Department, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania;2. Université de Lorraine, CRAN, UMR 7039, 2 av. Forêt de Haye, Vandœuvre-lès-Nancy, France;3. CNRS, CRAN, UMR 7039, 2 av. Forêt de Haye, Vandœuvre-lès-Nancy, France;1. Centre for Astroparticle Physics & Space Science and Department of Physics, Bose Institute, Kolkata, India;2. Variable Energy Cyclotron Centre, Kolkata, India;1. Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9, 040 01 Košice, Slovak Republic;2. Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011 Lviv, Ukraine;1. School of Science, Hubei University for Nationalities, Enshi, Hubei 445000, PR China;2. College of Computer Science, Civil Aviation Flight University of China, Guanghan, Sichuan 618307, PR China;1. Dipartimento di Ingegneria Scienze Informatiche e Matematica, Università dell’Aquila, via Vetoio (Coppito), I-67010 L’Aquila, Italy;2. Gran Sasso Science Institute (GSSI), I-67010 L’Aquila, Italy;3. School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332-0160, USA
Abstract:We consider a harmonic oscillator with delays. Linear stability is investigated by analyzing the associated characteristic transcendental equation. The bifurcation analysis of the equation shows that Hopf bifurcation can occur as the delay τ (taken as a parameter) crosses some critical values. The direction and stability of the Hopf bifurcation are considered by using the normal form theory due to Faria and Magalhães. An example is given to explain the results. Numerical simulations support our results.
Keywords:
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号