A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-...A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-cyclical pseudo-random sequences.However,the finite precision brings short period and odd points which obstruct application of chaos theory seriously in digital communication systems.Perturbation in chaotic systems is a possible efficient method for solving finite precision problems,but former researches are limited in uniform distribution maps.The proposed internal perturbation can work on both uniform and non-uniform distribution chaotic maps like Chebyshev map and Logistic map.By simulations,results show that the proposed internal perturbation extends sequence periods and eliminates the odd points,so as to improve chaotic performances of perturbed chaotic sequences.展开更多
For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg ...For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classica results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally.展开更多
For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power dis...For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power distributional chaos is exactly the usual distributional chaos. As a generalization of distributional n-chaos,λ-power distributional n-chaos is defined similarly. Lots of classic results on distributional chaos can be improved to be the versions of λ-power distributional n-chaos accordingly. A practical method for distinguishing 0-power distributional n-chaos is given. A transitive system is constructed to be 0-power distributionally n-chaotic but without any distributionally （n ＋ 1）-scrambled tuples. For each λ∈ [0, 1], ）,-power distributional n-chaos can still appear in minimal systems with zero topological entropy.展开更多
We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal sets.We show:i)an uncountable extremal di...We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal sets.We show:i)an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set:a periodic orbit with period 2;ii)an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets:a fixed point and an infinite minimal set;iii)infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set,and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits.展开更多
基金Supported by the National Basic Research Program of China(No.2007CB310606)
文摘A method of controllable internal perturbation inside the chaotic map is proposed to solve the problem in chaotic systems caused by finite precision.A chaotic system can produce large amounts of initial-sensitive,non-cyclical pseudo-random sequences.However,the finite precision brings short period and odd points which obstruct application of chaos theory seriously in digital communication systems.Perturbation in chaotic systems is a possible efficient method for solving finite precision problems,but former researches are limited in uniform distribution maps.The proposed internal perturbation can work on both uniform and non-uniform distribution chaotic maps like Chebyshev map and Logistic map.By simulations,results show that the proposed internal perturbation extends sequence periods and eliminates the odd points,so as to improve chaotic performances of perturbed chaotic sequences.
基金supported by National Natural Science Foundation of China(Grant Nos.11071084 and 11026095)Natural Science Foundation of Guangdong Province(Grant No.10451063101006332)+1 种基金the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province(Grant No.2012LYM 0133)Scientific Technology Planning of Guangzhou Education Bureau(Grant No.2012A075)
文摘For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classica results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally.
基金supported by the National Natural Science Foundation of China(Nos.11071084,11201157,11471125)the Natural Science Foundation of Guangdong Province(No.S2013040013857)
文摘For each real number λ∈ [0, 1], λ-power distributional chaos has been in- troduced and studied via Furstenberg families recently. The chaoticity gets stronger and stronger as A varies from 1 to 0, where 1-power distributional chaos is exactly the usual distributional chaos. As a generalization of distributional n-chaos,λ-power distributional n-chaos is defined similarly. Lots of classic results on distributional chaos can be improved to be the versions of λ-power distributional n-chaos accordingly. A practical method for distinguishing 0-power distributional n-chaos is given. A transitive system is constructed to be 0-power distributionally n-chaotic but without any distributionally （n ＋ 1）-scrambled tuples. For each λ∈ [0, 1], ）,-power distributional n-chaos can still appear in minimal systems with zero topological entropy.
基金supported by the Independent Research Foundation of the Central Universities(Grant No.DC 12010111)National Natural Science Foundation of China(Grant No.11271061)
文摘We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal sets.We show:i)an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set:a periodic orbit with period 2;ii)an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets:a fixed point and an infinite minimal set;iii)infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set,and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits.
