On Experimental Periodic Motions in a Duﬃng Oscillatory Circuit

Yu, Xiao‐Qi; Luo, Albert C. J.; Reyes, Zeltzin; Reyes-Munguía, Abigail; Goonesekere, Rojitha

doi:10.5890/jvtsd.2019.03.005

Cited by 9 publications

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“…Finally, the numerical investigation of the circuit's dynamics is presented. This investigation is based on the simulation results, which are produced by using numerical tools, such as phase portraits, maximal Lyapunov exponents [30][31][32][33], bifurcation diagrams [34], and continuation diagrams [35].…”

Section: Introductionmentioning

confidence: 99%

Antimonotonicity, Hysteresis and Coexisting Attractors in a Shinriki Circuit with a Physical Memristor as a Nonlinear Resistor

2022

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A novel approach to the physical memristor’s behavior of the KNOWM is presented in this work. The KNOWM’s memristor’s intrinsic feature encourages its use as a nonlinear resistor in chaotic circuits. Furthermore, this memristor has been shown to act like a static nonlinear resistor under certain situations. Consequently, for the first time, the KNOWM memristor is used as a static nonlinear resistor in the well-known chaotic Shinriki oscillator. In order to examine the circuit’s dynamical behavior, a host of nonlinear simulation tools, such as phase portraits, bifurcation and continuation diagrams, as well as a maximal Lyapunov exponent diagram, are used. Interesting phenomena related to chaos theory are observed. More specifically, the entrance to chaotic behavior through the antimonotonicity phenomenon is observed. Furthermore, the hysteresis phenomenon, as well as the existence of coexisting attractors in regards to the initial conditions and the parameters of the system, are investigated. Moreover, the period-doubling route to chaos and crisis phenomena are observed too.

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Section: Introductionmentioning

confidence: 99%

Antimonotonicity, Hysteresis and Coexisting Attractors in a Shinriki Circuit with a Physical Memristor as a Nonlinear Resistor

2022

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“…From the last century, the Duffing-type nonlinear dynamical systems have been investigated uninterruptedly in various fields conducted by plenty of researches, such as physics, engineering, chemistry, economics and biological and social sciences [12][13][14][15][16][17][18][19][20]. The effect of smooth single or multiple forces has been studied extensively in Duffing oscillator [12,13,[21][22][23][24][25]. Very few researchers reported about the applications of piecewise periodic linear forces [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Effect of Different Forms of Periodic Piecewise Linear Forces on Duffing Oscillator

et al. 2021

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The paper highlights the effect of different forms of periodic piecewise linear forces in the ubiquitous Duffing oscillator equation. The external periodic piecewise linear forces considered are Triangular, Hat, Trapezium, Quadratic and Rectangular. With the aid of some numerical simulation tools such as bifurcation diagram, phase portrait and Poincare´ map, the different routes to chaos and various strange attractors are found to occur due to the applied forces. The effect of an ε-parametric control force in the Duffing system is also analyzed. To characterize the regular and chaotic behaviours of this system, the maximal Lyapunov exponent is employed.

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Periodic Motions to Chaos in a Nonlinear Rotor System

Luo

2022

Nonlinear Systems and Complexity

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On Experimental Periodic Motions in a Duﬃng Oscillatory Circuit

Cited by 9 publications

References 0 publications

Antimonotonicity, Hysteresis and Coexisting Attractors in a Shinriki Circuit with a Physical Memristor as a Nonlinear Resistor

Antimonotonicity, Hysteresis and Coexisting Attractors in a Shinriki Circuit with a Physical Memristor as a Nonlinear Resistor

Effect of Different Forms of Periodic Piecewise Linear Forces on Duffing Oscillator

Periodic Motions to Chaos in a Nonlinear Rotor System

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