Dynamics of oscillators coupled by a medium with adaptive impact

Daneshvar, Roozbeh

doi:10.1002/cplx.21439

Cited by 7 publications

(5 citation statements)

References 55 publications

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“…This nonlinear core loss model shows the hysteresis effect better than the previous models. Also, Bifurcation diagram of this model also exhibits the dynamic behavior of the ferroresonance more clearly . Using this bifurcation diagram, one can analyze the complexity of trajectories.…”

Section: Nonlinear Core Losses Effectmentioning

confidence: 86%

Voltage transformer ferroresonance analysis using multiple scales method and chaos theory

et al. 2013

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In this article, the Multiple Scales Method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes subharmonic, quasi-periodic, and also chaotic oscillations. In this article, the chaotic behavior and various ferroresonant oscillations modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as Period Doubling Bifurcation (PDB), Saddle Node Bifurcation (SNB), Hopf Bifurcation (HB) and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via Multiple Scales Method obtaining Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

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Section: Nonlinear Core Losses Effectmentioning

confidence: 86%

Voltage transformer ferroresonance analysis using multiple scales method and chaos theory

et al. 2013

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“…Moreover, the application of fractional calculus in control theory has been widely reported [22][23][24][25][26]. Conversely, several scholars have shown increasing interest in the study of the problems related to the chaos and complexity [27][28][29][30][31]. However, to the best knowledge of the authors, there is little work in the literature about studying the dynamics of the fractional-order FOESDS and robust stabilization of the unstable corresponding system via fractional-order controllers.…”

Section: Examplementioning

confidence: 99%

Fractional modeling and control of a complex nonlinear energy supply‐demand system

Aghababa

2014

Complexity

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This article deals with the fractional‐order modeling of a complex four‐dimensional energy supply‐demand system (FOESDS). First, the fractional calculus techniques are adopted to describe the dynamics of the energy supply‐demand system. Then the complex behavior of the proposed fractional‐order FOESDS is studied using numerical simulations. It is shown that the FOESDS can exhibit stable, chaotic, and unstable states. When it exhibits chaos, the FOESDS's strange attractors are plotted to validate the chaotic behavior of the system. Moreover, we calculate the maximal Lyapunov exponents of the system to confirm the existence of chaos. Accordingly, to stabilize the system, a finite‐time active fractional‐order controller is proposed. The effects of model uncertainties and external disturbances are also taken into account. An estimation of the stabilization time is given. Based on the latest version of the fractional Lyapunov stability theory, the finite‐time stability and robustness of the proposed method are proved. Finally, two illustrative examples are provided to illustrate the usefulness and applicability of the proposed control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 74–86, 2015

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“…With the discovery of more and more fractional‐order systems, the problem of control of non‐integer‐order systems as well as the application of fractional‐based control techniques have been attracted the attention of many scholars . Furthermore, several scholars have shown increasing interest in the study of the problems related to the chaos and complexity .…”

Section: Introductionmentioning

confidence: 99%

Control of non‐integer‐order dynamical systems using sliding mode scheme

Aghababa

2015

Complexity

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This article deals with the problem of control of canonical non-integer-order dynamical systems. We design a simple dynamical fractional-order integral sliding manifold with desired stability and convergence properties. The main feature of the proposed dynamical sliding surface is transferring the sign function in the control input to the first derivative of the control signal. Therefore, the resulted control input is smooth and without any discontinuity. So, the harmful chattering, which is an inherent characteristic of the traditional sliding modes, is avoided. We use the fractional Lyapunov stability theory to derive a sliding control law to force the system trajectories to reach the sliding manifold and remain on it forever. A nonsmooth positive definite function is applied to prove the existence of the sliding motion in a given finite time. Some computer simulations are presented to show the efficient performance of the proposed chattering-free fractional-order sliding mode controller. V C 2015 Wiley Periodicals, Inc. Complexity 000: 00-00, 2015

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Dynamics of oscillators coupled by a medium with adaptive impact

Cited by 7 publications

References 55 publications

Voltage transformer ferroresonance analysis using multiple scales method and chaos theory

Voltage transformer ferroresonance analysis using multiple scales method and chaos theory

Fractional modeling and control of a complex nonlinear energy supply‐demand system

Control of non‐integer‐order dynamical systems using sliding mode scheme

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