Open AccessChaotic motion and control of the driven-damped Double Sine-Gordon equation
Author(s) -
Hang Zheng,
Yonghui Xia,
Manuel Pinto
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022037
Subject(s) - homoclinic orbit , chaotic , sine , chaos (operating system) , mathematics , sine gordon equation , motion (physics) , mathematical analysis , heteroclinic orbit , control theory (sociology) , classical mechanics , control (management) , physics , computer science , nonlinear system , geometry , bifurcation , computer security , soliton , quantum mechanics , artificial intelligence
In this paper, the chaotic motion of the driven and damped double Sine-Gordon equation is analyzed. We detect the homoclinic and heteroclinic chaos by Melnikov method. The corresponding Melnikov functions are derived. A numerical method to estimate the Melnikov integral is given and its effectiveness is illustrated through an example. Numerical simulations of homoclinic and heteroclinic chaos are precisely demonstrated through several examples. Further, we employ a state feedback control method to suppress both chaos simultaneously. Finally, numerical simulations are utilized to prove the validity of control methods.