A pair of van der Pol oscillators coupled by fractional derivatives

Suchorsky, M. K.; Rand, Richard H.

doi:10.1007/s11071-011-0266-1

Cited by 22 publications

(6 citation statements)

References 20 publications

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“…Due to the continuous order, fractional-order systems have independent frequency-domain and long memory transients [2,[5][6][7][8][9][10][11][12][13]59], which can describe complex physical system more accurately.…”

Section: Fractional-order Systemsmentioning

confidence: 99%

“…In recent years, researchers and engineers have increasingly used fractional-order dynamic models to model real physical systems that have independent frequency-domain and long memory transients [5][6][7][8][9][10][11][12][13]. Some systems may have fractional-order dynamic characteristics, even if each unit has integer-order dynamic characteristics [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Genetic Algorithm-Based Identification of Fractional-Order Systems

Zhou

Cao

Chen

2013

Entropy

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Abstract:Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.

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Section: Fractional-order Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Genetic Algorithm-Based Identification of Fractional-Order Systems

Zhou

Cao

Chen

2013

Entropy

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“…Switching of the system between different semi-stable attractors as well as chaotic beats have been observed. Suchorsky and Rand [18] have considered van der Pol oscillators coupled by fractional derivative. The authors have considered regions of locking and drifting and have demonstrated the reduction to known results in the limits where the fractional derivative is replaced by an integer.…”

Section: Introductionmentioning

confidence: 99%

Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators

et al. 2019

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Motivated by the dynamics of micro-scale oscillators with thermo-optical feedback, a simplified third order model, capturing the key features of these oscillators is developed, where each oscillator consists of a displacement variable coupled to a temperature variable. Further, the dynamics of a pair of such oscillators coupled via a linear spring is analyzed. The analytical procedures used are the variational equation method and the two-variable expansion method. It is shown that the analytical results are in agreement with the results of numerical integration. The bifurcation structure of the system is revealed through a bifurcation diagram.

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“…Fractional differential equations (FDEs) invoke the increasingly interesting to model the real-world problems in many fields, such as, material science, biology, engineering, and others [1,14,23]. The reason partly consists in that fractional derivatives can better describe frequency dependence and memory properties of various phenomena [3,18,11,24].…”

Section: Introductionmentioning

confidence: 99%