Hopf Bifurcations and Degeneracies in Chua’s Circuit a Perspective from a Frequency Domain Approach
نویسندگان
چکیده
In the present work explicit formulas for analyzing the birth of limit cycles arising in the Chua’s circuit through a Hopf bifurcation is provided. A local amplitude equation is derived using a frequency domain approach and harmonic balance approximations. Furthermore, the first Lyapunov index used to detect degenerate Hopf bifurcations is derived in terms of the parameters of the nonlinear circuit. A perspective for analyzing other bifurcations using this frequency domain approach is discussed.
منابع مشابه
Predicting Period-Doubling Bifurcations and Multiple Oscillations in Nonlinear Time-Delayed Feedback Systems
In this brief, a graphical approach is developed from an engineering frequency-domain approach enabling prediction of perioddoubling bifurcations (PDB’s) starting from a small neighborhood of Hopf bifurcation points useful for analysis of multiple oscillations of periodic solutions for time-delayed feedback systems. The proposed algorithm employs higher order harmonic-balance approximations (HB...
متن کاملA THREE DIMENSIONAL HTLV-1 MODEL WITH INTRACELLULAR AND IMMUNE ACTIVATION DELAYS
In this paper, a three dimensional mathematical model for HTLV-1infection with intracellular delay and immune activation delay is investigated.By applying the frequency domain approach, we show that time delays candestabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and sta-ble or unstable periodic oscillations. At the end, numerical simulations areillustrated.
متن کاملSome Results on Chua's equation Near a Triple-Zero Linear Degeneracy
In this work we study a wide class of symmetric control systems that has the Chua’s circuit as a prototype. Namely, we compute normal forms for Takens–Bogdanov and triple-zero bifurcations in a class of symmetric control systems and determine the local bifurcations that emerge from such degeneracies. The analytical results are used as a first guide to detect numerically several codimension-thre...
متن کاملThe mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures
The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency do...
متن کاملOn the Hopf-Pitchfork bifurcation in the Chua's equation
We study some periodic and quasiperiodic behaviors exhibited by the Chua’s equation with a cubic nonlinearity, near a Hopf–pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf–pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orb...
متن کامل