Homoclinic bifurcation and chaos control in MEMS resonators

The homoclinic bifurcation and chaos in a system of weakly coupled simple pendulum and harmonic oscillator subject to light dampings and weakly external and (or) parametric excitation of bounded noise is studied. The random Melnikov process is derived and mean-square criteria is used to determine the threshold amplitude of the bounded noise for the onset of chaos in the system. The threshold amplitude is also determined by vanishing the numerically calculated maximal Lyapunov exponent. The threshold amplitudes are further confirmed by using the Poincaré maps, which indicate the path from periodic motion to chaos or from random motion to random chaos in the system as the amplitude of bounded noise increases.

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Stability, Bifurcation, and Chaos inN-Firm Nonlinear Cournot Games

Discrete Dynamics in Nature and Society ◽

10.1155/2011/380530 ◽

2011 ◽

Vol 2011 ◽

pp. 1-22 ◽

Cited By ~ 7

Author(s):

Akio Matsumoto ◽

Ferenc Szidarovszky

Keyword(s):

Chaos Control ◽

Adjustment Process ◽

Bifurcation And Chaos ◽

Adaptive Expectations ◽

Special Cases ◽

Adaptive Adjustment ◽

Cournot Games ◽

Best Responses ◽

Linear Cost ◽

Shed Light

AnN-firm production game known as oligopoly will be examined with isoelastic price function and linear cost under al Cournot competition. After the best responses of the firms are determined, a dynamic system with adaptive expectations is introduced. It is first shown that the local asymptotic behavior of the system is identical with that of the adaptive adjustment process in which the firms cautiously determine their outputs. Dynamic analysis is confined to two special cases, one in whichNis divided into two groups and the other in whichNis divided into three groups. Then stability conditions will be derived and the global behavior of the equilibria will be illustrated including chaos control. Lastly the two- and three-group models are compared with two-firm (duopoly) and three-firm (triopoly) models to shed light on roles of the number of the firms.

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Stability, Neimark-Sacker bifurcation and chaos control for a prey-predator system with harvesting effect on predator

Miskolc Mathematical Notes ◽

10.18514/mmn.2021.3450 ◽

2021 ◽

Vol 22 (2) ◽

pp. 663

Author(s):

Özlem Ak Gümüş ◽

Michal Fečkan

Keyword(s):

Chaos Control ◽

Bifurcation And Chaos ◽

Predator System

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Feed-Forward Slope Compensated PFC for Chaos Control

Journal of Circuits System and Computers ◽

10.1142/s0218126615500656 ◽

2015 ◽

Vol 24 (05) ◽

pp. 1550065 ◽

Cited By ~ 1

Author(s):

Ya-Ni Li ◽

Yin-Tang Yang ◽

Zhang-Ming Zhu ◽

Chao-Lin Zhang

Keyword(s):

Chaos Control ◽

Current Mode ◽

Response Speed ◽

System Stability ◽

Nonlinear Phenomena ◽

Bifurcation And Chaos ◽

Feed Forward ◽

Loop Control ◽

Circuit Structure ◽

Slope Compensation

Based on the dual-loop control peak current mode power factor correction (PFC) converter, a feed-forward slope compensation method is proposed, which could regulate the compensated slope real-time and suppress the loop perturbation, thus controlling chaos of the system for better stability. A dual-loop Boost PFC model with the feed-forward slope compensation is built to analyze the nonlinear phenomena in system, and the corresponding circuit structure is presented. The chaos control ability of the feed-forward slope compensation is studied theoretically, and the relation of compensated slope and feed-forward signal is deduced, as well as slope stability conditions. The simulation and measured results show that this method could effectively suppress system bifurcation and chaos phenomena, and improve the system working range and dynamic response speed, and eliminate the influence on system stability for without compensated, under compensated, and over compensated.

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