In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and pr...In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.展开更多
When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical ...When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.展开更多
A change in neuronal-action potential can generate a magnetically induced current during the release and propagation of intracellular ions.To better characterize the electromagnetic-induction effect,this paper present...A change in neuronal-action potential can generate a magnetically induced current during the release and propagation of intracellular ions.To better characterize the electromagnetic-induction effect,this paper presents an improved discrete Rulkov(ID-Rulkov)neuron model by coupling a discrete model of a memristor with sine memductance into a discrete Rulkov neuron model.The ID-Rulkov neuron model possesses infinite invariant points,and its memristor-induced stability effect is evaluated by detecting the routes of period-doubling and Neimark-Sacker bifurcations.We investigated the memristor-induced dynamic effects on the neuron model using bifurcation plots and firing patterns.Meanwhile,we theoretically expounded the memristor initial-boosting mechanism of infinite coexisting patterns.The results show that the ID-Rulkov neuron model can realize diverse neuron firing patterns and produce hyperchaotic attractors that are nondestructively boosted by the initial value of the memristor,indicating that the introduced memristor greatly benefits the original neuron model.The hyperchaotic attractors initially boosted by the memristor were verified by hardware experiments based on a hardware platform.In addition,pseudorandom number generators are designed using the ID-Rulkov neuron model,and their high randomness is demonstrated based onstrict test results.展开更多
Chaotic systems are an effective tool for various applications, including information security and internet of things. Many chaotic systems may have the weaknesses of incomplete output distributions, discontinuous cha...Chaotic systems are an effective tool for various applications, including information security and internet of things. Many chaotic systems may have the weaknesses of incomplete output distributions, discontinuous chaotic regions, and simple chaotic behaviors.These may result in many negative influences in practical applications utilizing chaos. To deal with these issues, this study introduces a modular chaotification model(MCM) to increase the dynamic properties of current one-dimensional(1 D) chaotic maps. To exhibit the effect of the MCM, three 1 D chaotic maps are improved using the MCM as examples. Studies of the resulting properties show the robust and complex dynamics of these improved chaotic maps. Moreover, we implement these improved chaotic maps of MCM in a field-programmable gate array hardware platform and apply them to the application of PRNG. Performance analyses verify that these chaotic maps improved by the MCM have more complicated chaotic behaviors and wider chaotic ranges than the existing and several new chaotic maps.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 60973162)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009GM037)+1 种基金the Science and Technology of Shandong Province, China(Grant No. 2010GGX10132)the Key Program of the Natural Science Foundation of Shandong Province, China (Grant No. Z2006G01)
文摘In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandorn number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFB0802000)the Cryptography Theoretical Research of National Cryptography Development Fund,China(Grant No.MMJJ20170109).
文摘When chaotic systems are implemented on finite precision machines, it will lead to the problem of dynamical degradation. Aiming at this problem, most previous related works have been proposed to improve the dynamical degradation of low-dimensional chaotic maps. This paper presents a novel method to construct high-dimensional digital chaotic systems in the domain of finite computing precision. The model is proposed by coupling a high-dimensional digital system with a continuous chaotic system. A rigorous proof is given that the controlled digital system is chaotic in the sense of Devaney's definition of chaos. Numerical experimental results for different high-dimensional digital systems indicate that the proposed method can overcome the degradation problem and construct high-dimensional digital chaos with complicated dynamical properties. Based on the construction method, a kind of pseudorandom number generator (PRNG) is also proposed as an application.
基金supported by the National Natural Science Foundation of China(Grant Nos.62271088 and 62201094)the Scientific Research Foundation of Jiangsu Provincial Education Department,China(Grant No.22KJB510001)。
文摘A change in neuronal-action potential can generate a magnetically induced current during the release and propagation of intracellular ions.To better characterize the electromagnetic-induction effect,this paper presents an improved discrete Rulkov(ID-Rulkov)neuron model by coupling a discrete model of a memristor with sine memductance into a discrete Rulkov neuron model.The ID-Rulkov neuron model possesses infinite invariant points,and its memristor-induced stability effect is evaluated by detecting the routes of period-doubling and Neimark-Sacker bifurcations.We investigated the memristor-induced dynamic effects on the neuron model using bifurcation plots and firing patterns.Meanwhile,we theoretically expounded the memristor initial-boosting mechanism of infinite coexisting patterns.The results show that the ID-Rulkov neuron model can realize diverse neuron firing patterns and produce hyperchaotic attractors that are nondestructively boosted by the initial value of the memristor,indicating that the introduced memristor greatly benefits the original neuron model.The hyperchaotic attractors initially boosted by the memristor were verified by hardware experiments based on a hardware platform.In addition,pseudorandom number generators are designed using the ID-Rulkov neuron model,and their high randomness is demonstrated based onstrict test results.
基金supported by the National Natural Science Foundation of China (Grant No. 62071142)the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (Grant No. HIT.NSRIF.2020077)。
文摘Chaotic systems are an effective tool for various applications, including information security and internet of things. Many chaotic systems may have the weaknesses of incomplete output distributions, discontinuous chaotic regions, and simple chaotic behaviors.These may result in many negative influences in practical applications utilizing chaos. To deal with these issues, this study introduces a modular chaotification model(MCM) to increase the dynamic properties of current one-dimensional(1 D) chaotic maps. To exhibit the effect of the MCM, three 1 D chaotic maps are improved using the MCM as examples. Studies of the resulting properties show the robust and complex dynamics of these improved chaotic maps. Moreover, we implement these improved chaotic maps of MCM in a field-programmable gate array hardware platform and apply them to the application of PRNG. Performance analyses verify that these chaotic maps improved by the MCM have more complicated chaotic behaviors and wider chaotic ranges than the existing and several new chaotic maps.
