Discrete‐time dynamic image segmentation based on oscillations by destabilizing a fixed point

Fujimoto, Ken’ichi; Kobayashi, Mio; Yoshinaga, Tetsuya

doi:10.1002/tee.20683

Cited by 4 publications

(3 citation statements)

References 9 publications

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“…In nonlinear periodic systems with a long time period, the modified Poincaré map (second-order Poincaré map) is a candidate for studying the chaos phenomenon in the systems. This map converts the dynamical equations of the system to discrete recursive relations [7]. Since chaotic systems naturally have a continuous, broad spectrum [8], the conventional spectral analysis is an inaccurate and insecure method for fault identification.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov exponent and bifurcation characteristics in synchronous machines with an internal fault

Shariatmadar¹,

Nazarzadeh²,

Abedi³

2013

IEEJ Transactions Elec Engng

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In this paper, first, turn-to-turn fault in a synchronous machine stator winding is investigated, and its inductances are derived with the winding function method. Then, using the nonlinear control theory, the first-order Poincaré map of the synchronous machine is computed, and a new extended Poincaré map of the machine is established. Also, the characteristic multipliers of the synchronous machine are calculated by the Poincaré map. This new map is capable of analyzing electrical machines in the nonlinear and unbalanced cases for evaluation of stability, bifurcation, and chaos phenomena. The results show that the new map is an effective technique for modeling and analyzing any AC electrical machines. The characteristic multipliers and the Lyapunov exponents of the extended map indicate the system's condition. Chaotic phenomena are observed in some machines with internal faults. Since chaotic systems have a continuous spectrum and various kinds of frequencies in their spectrum, identification of the internal fault location is not easy with harmonic analyses such as Fourier spectrum method on the excitation current in synchronous machines.

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Section: Introductionmentioning

confidence: 99%

Lyapunov exponent and bifurcation characteristics in synchronous machines with an internal fault

Shariatmadar¹,

Nazarzadeh²,

Abedi³

2013

IEEJ Transactions Elec Engng

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“…In this study, we investigated a novel discrete-time coupled model comprising one-dimensional oscillators based on the Rulkov map [13] and a globally coupled oscillator. The coupled model had 1 N + dimensions and a network structure similar to that of the dynamic image segmentation system proposed in our previous studies [14]- [16]. The new model used adaptive coupling to extract image regions in which the pixel values change gradually.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Dynamic Image Segmentation Using Oscillators with Adaptive Coupling

Kobayashi¹,

Yoshinaga²

2016

IJMNTA

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In this study, we propose a novel discrete-time coupled model to generate oscillatory responses via periodic points with a high periodic order. Our coupled system comprises one-dimensional oscillators based on the Rulkov map and a single globally coupled oscillator. Because the waveform of a one-dimensional oscillator has sharply defined peaks, the coupled system can be applied to dynamic image segmentation. Our proposed system iteratively transforms the coupling of each oscillator based on an input value that corresponds to the pixel value of an input image. This approach enables our system to segment image regions in which pixel values gradually change with respect to a connected region. We conducted a bifurcation analysis of a single oscillator and a three-coupled model. Through simulations, we demonstrated that our system works well for graylevel images with three isolated image regions.

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“…This means that the OGY method can be used to recover desired behavior destabilized by bifurcations from an undesirable state. For example, by using ideas of controlling chaos, we previously proposed a recovery system [13] for a dynamic image-segmentation system consisting of a discrete-time oscillator network [14,15].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation avoidance control of stable periodic points using the maximum local Lyapunov exponent

Fujimoto

Aihara

2015

NOLTA

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We propose a novel controlling methodology for avoiding local bifurcations of stable, hyperbolic fixed and periodic points in nonlinear discrete-time dynamical systems with parameter variation. Dynamical systems may not work as expected owing to bifurcations of desired behavior caused by parameter variation. Controlling parameters to avoid bifurcations enables us to construct robust dynamical systems against unexpected parameter variation. Assuming that desired behavior is a hyperbolic fixed or periodic point, as a control strategy, optimizing the degree of its stability (i.e. the maximum modulus of its characteristic multipliers) is considerable. However, it cannot be optimized by simple gradient methods, and off-line calculation to find the exact positions of fixed and periodic points and their characteristic multipliers is also needed. In contrast, the method we propose is to control the maximum local Lyapunov exponent (MLLE) that is defined in finite time and is closely related to the degree of stability on hyperbolic fixed and periodic points. This method can predict occurrence of local bifurcations for parameter variation by monitoring the MLLE along the passage of time and adjust parameter values on line to control the MLLE. This leads that occurrence of local bifurcations can be avoided without directly analyzing bifurcations in advance. The parameter regulation to avoid local bifurcations is theoretically derived from the minimization of an objective function with respect to the MLLE. Our experimental results applied to the Kawakami and Hénon maps demonstrate that the proposed controller could be used to avoid local bifurcations.

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Discrete‐time dynamic image segmentation based on oscillations by destabilizing a fixed point

Cited by 4 publications

References 9 publications

Lyapunov exponent and bifurcation characteristics in synchronous machines with an internal fault

Lyapunov exponent and bifurcation characteristics in synchronous machines with an internal fault

Discrete-Time Dynamic Image Segmentation Using Oscillators with Adaptive Coupling

Bifurcation avoidance control of stable periodic points using the maximum local Lyapunov exponent

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