Research On The Combined System Based On 1D Discrete Chaotic Maps

Chaotic systems have many characteristics,such as initial value sensitivity,unpredictability and topological mixing.These valuable properties make chaotic systems widely studied and applied in many aspects.When chaotic systems are applied in practice,some existing chaotic systems have limited dynamic characteristics.On the one hand,there are some techniques can evaluate the dynamic behavior of many existing chaotic systems by identifying initial states or estimating chaotic signals.On the other hand,chaos degradation occurs when chaotic behavior is simulated on some finite precision platforms.This will degrade chaotic behavior to periodic behavior,therefore,the chaos-based application is negatively affected.Some chaotic systems only generate chaos in some isolated parameter interval,and a slight disturbance to the parameter will cause the parameter to fall into the non-chaotic region,thus destroying the chaos.Therefore,designing a chaotic system with more complex dynamic behavior becomes the focus of research.This thesis focuses on a combined system based on 1D discrete chaotic maps.Some simple 1D discrete chaotic maps are used to combine the chaotic systems to obtain better chaotic characteristics.The main research work and innovations can be summarized as follows:(1)In order to obtain a chaotic system with larger Lyapunov exponent(LE)and wider chaotic range,a parallel combined model is proposed.This model parallels some simple chaotic maps,whose structure is relatively simple,more convenient for hardware implementation.By increasing the control parameters,the sequence generated by the parallel combined model can improve the LE and chaotic range as much as possible.The performance evaluation shows that the dynamic complexity of the chaotic map generated by the new model is higher.In order to demonstrate the application of discrete chaotic system in engineering,we use the new system for image encryption,and the results show that the sequence generated by the new system is more secure.(2)Considering the sensitivity of chaos map to initial value,a new combined chaotic system based on max function is proposed by adding a small enhancement variable.A unified method was found to enhance any 1D discrete chaotic map.The chaotic region of the original map becomes a part of the improved map.When the small enhancement variable appeare in the nonlinear term,its LE will increase to a certain extent.Finally,the effectiveness of the system was verified by theoretical analysis and numerical simulation.