| In the field of nonlinear science,the study of pattern dynamics of nonlinear systems,spatiotemporal chaos control and synchronization has always been a hot topic.In particular,there are still many problems to be solved in the study of spatiotemporal chaos in photorefractive ring oscillators for its typical nonlinear characteristics.The research space of this system is broad and the application potential is huge.Based on the dynamics of photorefractive ring oscillator,the spatiotemporal of chaos control and synchronization in the photorefractive ring oscillators is sudied numerically by the coupled map lattice model.The control and synchronization methods are constant offset,phase space compression,feedback,coupling and modulation.The regularities of chaos control and synchronization are summarized and the effective method of chaos control and synchronization is finded.The dissetation is divided into three parts.The first part is the construction of the one and two dimensional spatial expansion model of a photorefractive ring oscillator,the analysis of photorefractive ring oscillator system dynamics behavior.The second part is the effective control of spatiotemporal chaos in one and two dimensional space extended model.The third part is the studey of the synchronization of spatiotemporal chaos in a system of two or more photorefractive ring oscillators in one and two dimensional space.In the first part,it is introduced for the research progress of chaos control and chaos synchronization in optics,the photorefractive effect mechanism,kinetic equation,the latest progress,research methods,the basic research model of spatiotemporal chaos control and synchronization of photorefractive ring oscillator system.Dynamic equation of photorefractive ring oscillator is derivated based on general dynamics equation of nonlinear optical system.The stability of photorefractive ring oscillator is analysed.The transverse pattern of one dimension and two dimensional extended model of the system is studied based on the bifurcation and chaos output of the photorefractive ring oscillation system.Finally,through numerical simulation,evolution progress from symmetry breaking to optical turbulence is gived and it's proved that this transformation mechanism is collective effect of the specific boundary conditions,initial conditions,the nonlinear interaction of system coupling and spatial diffraction results.In the second part,the control methods of chaos in one dimension and two dimensional space of a photorefractive ring oscillator are studied.In this dessitation,the stability control of spatiotemporal chaos in a photorefractive ring oscillator system is realized by five different methods of constant deviation,phase space compression,linear feedback method,nonlinear feedback method and periodic signal modulation method.By using the constant deviation method,the chaotic state in the system can be controlled to the stable periodic orbit,and the control effect is ideal by properly choosing the migration intensity.The research shows that the control regularyty of the two dimensional space is similar to that of one dimensional space when the system is controlled by the method of constant deviation.The control of spatiotemporal chaos in a photorefractive ring oscillator system can be achieved by selecting the appropriate compression intensity.The numerical simulation results show that the compression intensity has extreme value.When the limit value is exceeded,the phase space compression method will be invalid.In addition,the phase space compression method is also an ideal control effect in the local area control.For the linear feedback control method,by adjusting the system feedback light intensity and feedback coefficient,the system can be controlled to the stable periodic orbits from a chaotic state,and there is a minimum value and the maximum value of the feedback light intensity feedback coefficient to achieve control of spatiotemporal chaos.The method will be failure beyond the scope.For the nonlinear feedback method,the optical spatiotemporal chaos in a photorefractive ring oscillator system can be cotrolled to a uniform steady state or a time period by an appropriate selection of the feedback intensity.Signal modulation method to control chaos of the space of a photorefractive ring oscillator is proposed in the dessitation.By using an external sinusoidal signal as modulation signal,the photorefractive ring oscillator system can be controlled to stabilize the spatiotemporal periodic state,and the frequency of the output signal is determined by the modulation frequency.In the third part,the spatiotemporal chaos synchronization of two photorefractive ring oscillators is studied in one dimension and two dimension space.In this dessitation,the mutual coupling,one-way coupling,nonlinear feedback method and signal modulation method are used to synchronize the two photorefractive ring oscillator systems.The nonlinear feedback method is used to realize the accurate chaotic synchronization in the two the photorefractive ring oscillator system with different initial conditions.It is proved that the feedback strength can be improved to overcome the noise interference and improve the accuracy of the system.The mutual coupling method can be also used to achieve accurate synchronization in photorefractive ring oscillator system with two different initial conditions.But no matter how to change the value of coupling strength,the systems can not be controlled to synchronization in period 1 state.The effect of system errors and noise on the synchronization effect is studied and it's proved that this method is robust.The periodic modulation method is proposed for the first time to synchronize two-dimensional spatiotemporal chaos in two photorefractive ring oscillator.Two systems can achieve period synchronization by period signal modulation,and two dimensional spatiotemporal chaos synthronization is achieved by the random signal and the chaotic signal only when the adjustment intensity is large enough. |
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