Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System
نویسندگان
چکیده
In this paper, a new four-dimensional (4D) hyperchaotic biplane system is designed and presented. The dynamical properties of are studied by means tools such as bifurcation diagrams, Lyapunov exponents phase diagrams. Hopf periodic solutions solved analytically. addition, control strategy applied, comparative analysis the controlled performed.
منابع مشابه
HOPF BIFURCATION CONTROL WITH PD CONTROLLER
In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
متن کاملHopf Bifurcation for a New Chaotic System
In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given. Keyw...
متن کاملControl of a Hyperchaotic System Via Generalized Backstepping Method
This paper investigates on control and stabilization of a new hyperchaotic system. The hyperchaotic system is stabilized using a new technique which called Generalized Backstepping Method (GBM). Because of its similarity to Backstepping approach, this method is called GBM. But, this method is more applicable in comparison with conventional Backstepping. Backstepping method is used only for sy...
متن کاملThe Quasi-Periodic Reversible Hopf bifurcation
We consider the perturbed quasi-periodic dynamics of a family of reversible systems with normally 1:1 resonant invariant tori. We focus on the generic quasi-periodic reversible Hopf bifurcation and address the persistence problem for integrable quasiperiodic tori near the bifurcation point. Using kam theory, we describe how the resulting invariant tori of maximal and lower dimensions are parame...
متن کاملA New Modified Hyperchaotic Finance System and its Control
In this letter, a new four-dimensional continuous autonomous hyperchaotic system, which is constructed based on a modified finance system by introducing a nonlinear state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including equlibria and stability, various attractors, bifurcation analysis, and Lyapunov exponents spectrum. Furtherm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2023
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math11122699