Network Analysis Of Dynamics Of Chaotic Systems In Digital Domain

Chaotic systems are extensively used to design true random number generators,pseudo-random number generators and secure communication algorithms.However,in the digital world,the dynamic properties of the chaotic systems must be degraded to varying degrees due to the finite-precision effect.Understanding and controlling the dynamic properties are related to the basis of any chaos-related application.This thesis focuses on the dynamic properties of low-dimensional chaotic maps implement-ed in the digital domain.The state-mapping network corresponding to a chaotic map is established by the following way:every representable value in the definition domain of the chaotic map is considered as a node,while a directed edge between a pair of nodes is built if and only if the former node is mapped to the latter one by the chaotic map.Then,the dynamic degradation of the corresponding chaotic map was studied by the relationship between the state-mapping network(SMN)and implementation precision.The study on the dynamics of digital chaotic systems involves one-dimensional Logistic map,Tent map and two-dimensional Cat map.The main achievements contained in this thesis are as follows:1.First,we review the existing related studies of the topic and present some general properties between SMN and the implementation precision of iterative chaotic maps.Then,we prove the scale-free property of SMN of the Logistic map in fixed-point arithmetic domain and analyzes specific impact of floating-point operation mode on Logistic map.The strong correlation between the SMNs of Logistic map obtained with the two arithmetic mode is given.2.To further disclose the influence of the nature of chaotic map on the structure of SMN,we extends the analysis to Tent map and compare the differences of SMNs of the two chaotic map in the same arithmetic domain.3.Finally,we further study how SMN of two-dimensional Cat map change as in-crease of implementation precision and clarify the specific relationship between the cycle distribution of 2-D Cat map and the structure of its SMN.The obtained results of this thesis are helpful to understand the real structure of digital chaotic system in the finite-precision arithmetic domain and may promote more effective resistance and accurate evaluation of the dynamical degradation of the digital chaotic systems.