复值激光环形网络的振幅控制与混沌同步

IF 3.3 3区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractals-Complex Geometry Patterns and Scaling in Nature and Society Pub Date : 2023-08-28 DOI:10.1142/s0218348x23500913

Lin Chai, Jian Liu, Guanrong Chen, Xiaotong Zhang, Yiqun Li

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引用次数: 0

摘要

许多真实世界的系统在自然和人造网络中连接在一起。一个复值激光网络可以模拟人脑的工作机制。然而，复值激光网络的振幅控制很少被研究。本文研究了复值洛伦兹激光系统的环形网络。环网络表现出复杂的动力学，包括超混沌、准周期轨道和共存的超混沌。在环网络中，通过改变或不变的李雅普诺夫指数实现了三种面向单参数的幅度控制。同时，一个简单的旋钮可以实现超混沌信号的幅度重缩放，降低了电路实现成本。此外，对于具有强耦合的网络，建立了所有节点之间的混沌完全同步准则。对于相对较弱的耦合，找到了准周期完全同步，并从互相关系数的角度研究了混沌同步的性能。研究还表明，对于相同规模的激光网络，同步性能的改善和趋势对节点数的奇偶性是鲁棒的。

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AMPLITUDE CONTROL AND CHAOTIC SYNCHRONIZATION OF A COMPLEX-VALUED LASER RING NETWORK

Many real-world systems are connected together, in natural and man-made networks. A complex-valued laser network can simulate the working mechanism of human brain. However, amplitude control of a complex-valued laser network is seldom studied. In this paper, a ring network of complex-valued Lorenz laser systems is investigated. The ring network exhibits complex dynamics including hyper-chaos, quasi-periodic orbits, and coexisting hyper-chaos. Three kinds of single-parameter oriented amplitude controls are realized with varying or unvarying Lyapunov exponents in the ring network. Meanwhile, a simple knob can realize the amplitude rescaling of hyper-chaotic signals, which reduces the cost of circuit implementation. Moreover, a criterion of chaotic complete synchronization among all the nodes is established for a network with strong coupling. For relatively weak coupling, quasi-periodic complete synchronization is found, and the performance of chaotic synchronization is studied in terms of the cross-correlation coefficient. It is moreover revealed that the improvement and trend of synchronization performance are robust to the parity of the number of nodes for the same-scale laser networks.

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来源期刊

Fractals-Complex Geometry Patterns and Scaling in Nature and Society 数学-数学跨学科应用

CiteScore

7.40

自引率

23.40%

发文量

319

审稿时长

>12 weeks

期刊介绍： The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes. Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality. The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.