| Nonlinear dynamics has been widely applied in many fields such as natural sciences,social sciences,and engineering technology.The introduction of nonlinear dynamic theory into the field of image processing is a new way of application of nonlinear dynamics theory,and also a new approach to image processing.Based on the theory of fractional-order nonlinear dynamics and synchronous control,we research and analyze the dynamic characteristics of some new nonlinear systems,and explore the meeting point between the dynamic characteristics of the nonlinear system and image processing model to construct an image processing model.Using nonlinear dynamic characteristics to construct new models,it can broaden the application of nonlinear theory.Such a model constructed can simulate the internal work mechanisms of human perceptual system and provide a new explanation for the internal mechanisms.Forementioned researching works have a theoretical significance and application prospects both in the field of image processing and neurodynamics.The main works and innovations of this dissertation include the following aspects:(1)Based on fractional-order Chua’s system and fractional-order Chua-Hartly’s system,two kinds of fractional-order complex systems of Chua’s(time-delay)system and Chua-Hartly’s system are constructed respectively.The dynamical behavior of the two kinds of complex systems are discussed in detail by using phase diagram,bifurcation diagram and largest Lyapunov exponent.To get the calculus method of the complex number differential,we extend the fractional differential calculus to complex number and simulate the fractional-order complex Chua’s(time-delay)system.To get the fractionalorder complex Chua-Hartly’s system,we convert a complex system into 6 variable real system.For analyzing the new systems,we change the order of the system and have observed rich dynamic behaviors such as different periodic windows,single scroll,multiperiod.As the end of this work,we discuss the similarities and differences between two forementioned kinds of complex system dynamic behavior,alos the relationship between the dynamic behavior of fractional order system and the construction of image processing model.(2)Based on the stability analysis theory of fractional-order systems,the stability and oscillatory domains of fractional-order Relaxation oscillator are investigated with different external stimulus.Combined with the analysis of phase diagram and bifurcation diagram,the oscillation is found to be rhythmic oscillation.Using the rhythm oscillation characteristics of fractional-order Relaxation oscillator,an image enhancement model is constructed and its effectiveness is demonstrated by experiments.Firstly,the stability analysis method of fractional-order system is used to analyze the stability of the equilibriums of fractional Relaxation oscillator with different external stimulus.Combining the results of analysis of bifurcation diagram,the range of external stimulus which it can make the fractional-order Relaxation oscillator oscillate in rhythm is determined.For different external stimulus,the characteristics of oscillation produced by the fractional-order system are different.Based on this characteristics,a Quasi Gamma Curve(QGC)Model is constructed for enhancing the underexposure and overexposure images.The performance of the improved image enhancement based on QGC model is compared with other similar algorithms.In addition,the image enhancement model may similuate the mechanism which the human visual system can adapt to different lighting conditions.(3)Based on the active control method of fractional chaotic systems and the strategy of time-sharing synchronization,a scheme is designed with a controller for realizing the time-division phase synchronization between the drive sytems(part of complex network)and response system(single chaotic system).Using this scheme,an object selection model is constructed and its feasibility is verified by experiments;Introducing the fractionalorder active control strategy and time-division synchronization strategy,the sub networks are converted to a hybrid system by linear accumulative to achieve the time-division phase synchronization with single fractional-order system.Thus,an object selection model including two layers is built,which composed control unit and image segmentation unit.The first layer of the model is composed coupled oscillators with each other and used to implement image segmentation by phase synchronization.The central unit consisting of an oscillator,achieves the synchronization with different sub networks representing different objects at different time to realize the object selection function of the proposed model.In addition,time-sharing phase synchronization may be the mechanism of human visual selection and shifting.(4)Based on the stability theory of fractional-order systems,a projective synchronization scheme,in which the coefficients are different,is realized in 1+N complex networks with fractional-order complex variable nodes.This complex function projection synchronization scheme can be used to build a model to recognize image fractal features,and the simulation results show that the method is feasible.Firstly,a drive-response system composed by complex networks with 1+N nodes is constructed,in which the nodes are fractional-order complex chaotic systems.Base on the stability theory of fractional-order system,a model is designed with reasonable controllers to realize the function projection synchronization with different projection coefficients,and the coefficients of the function projection are used as an encoder to encode the fractal features.Then using the properties of projective synchronization error system,the input variables for identifying fractal features are solved and the fractal features can be recognized.In addition,the proposed schemem is also a good understanding for the recognition function in human perception systems. |
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