There are a large number of nonlinear systems in nature and human society. Chaos, as a non-periodic solution in deterministic nonlinear dynamic systems, has long been considered harmful and needs to be suppressed. This is because chaos is a non-linear dynamical system that is sensitive to initial values, unpredictable, and similar to randomness, and people do not know enough about it. However, through in-depth research on the theory behind chaotic phenomena, scholars found that chaos is controllable and synchronizable, and through the combination of nonlinear circuits and chaos theory, it is possible to apply chaos theory to the field of electronic communications and other engineering , This historic discovery is a milestone for the development of chaos theory and applications [1].

With countless researchers studying chaos theory in depth and broadening the boundaries of chaos application, the charm of the scientific beauty described by chaos theory and its related application prospects is blooming brightly. As Professor Leon O. Chua described: "In the history of science and technology, chaos has never been like a phenomenon. It is almost everywhere. It is both a universal example and a multidisciplinary research field. At present. , The exploration of chaos is only on the surface of a steep iceberg. Under this iceberg, there are all kinds of extremely beautiful structures with infinite complexity, like a tortuous and endless geometric maze or a surreal The connotation and profound beauty that is fascinating." [1-3]

Study the meaning of chaos

The iconic event that chaos can be applied in practice is the discovery of a chaos control method proposed by American physicists E.Ott, G.Grebogi and JAYorke in 1990[4], and the discovery by LMPecora and TLCarrol of the US Naval Laboratory The phenomenon of self-synchronization of chaos existing in the circuit [5]. Therefore, since the 1990s, the research on chaos control has become a hot topic in chaos research, attracting a large number of researchers to join. The application potential of chaos in secure communication makes the research on chaos rise to a new height. Chaos research has many theoretical and practical significances:

(1) The discovery of chaotic motion and the popularization of chaotic theory have made chaos, a form of motion that has been common in nature and has been neglected for a long time, to be recognized and understood. This motion can explain many incomprehensible phenomena in the past.

(2) The discovery of chaotic motion provides people with a new thinking angle for thinking about problems. Such as the problem of long-term weather forecasting, the discovery of the Lorentz attractor, and the sensitivity of the solution of atmospheric dynamics equations to initial values have shaken the original idea that long-term weather forecasting can be solved by improving the calculation accuracy. The ergodic nature of the chaotic attractor can just guarantee the stability of many long-term average quantities and the independence of initial conditions.

(3) Research on chaotic motion can inspire how to use precise scientific methods such as mathematics and physics to study complex life phenomena. For example, mathematical models such as coupled nonlinear oscillators can be used to simulate and cooperate with physiological experiments, which can reveal the possible connection of various arrhythmia, atrioventricular conduction obstruction, ventricular fibrillation and chaotic motion.

(4) The study of chaos has changed man’s understanding of nature. For a long time, there have been two completely opposite systems in the description of nature, namely the deterministic system and the probability theory system. Classical Newtonian mechanics is a strong support for the deterministic system and describes probability theory as a supplementary theory of last resort. The research findings of chaotic motion show that determinism and randomness can be unified (the inherent randomness of deterministic systems), so that the two theoretical description systems do not have to be completely opposed, and the unity of nature can be more fully understood and understood by people .

(5) Some characteristics of chaos, such as sensitivity to initial values, nonlinearity, randomness-like, and simple structure of chaotic systems can produce complex dynamics, which are especially suitable for chaotic secure communication and image encryption. The realization of chaotic synchronization proves that this application direction is feasible, and provides a new tool for the safe and reliable transmission of data in the modern information society.

Research Outlook

In recent years, the development of artificial intelligence has been very rapid, and one of the important research areas is artificial neural networks. Artificial neural network is a mathematical or physical abstraction and simulation of some basic characteristics of biological neural networks. It is an intelligent bionic model based on connection theory. A large number of neurophysiological and neuroanatomical studies have confirmed that there is chaos in the human brain, and studies have shown that normal brain waves are in a state of chaos [3]. . Therefore, in recent years, the research and analysis of chaotic phenomena or chaotic dynamics in (artificial) neural networks has become a hot topic [6-10].

With the support of chaos theory, it will be helpful in the future to study the potential causes of different mental illnesses by combining different technical means, for example, what interference or stimulus factors make the brain waves in a normal chaotic state deviate from the original operating law and cause nerves System disorder. It is precisely because chaos is omnipresent and blends with traditional disciplines. Under the advanced technology system spawned by modern artificial intelligence, perhaps in the near future, with the help of chaos theory, many unsolved mysteries can be completely solved. Related cross-researches are endless. Imagine and apply space. Because chaotic signal has the characteristics of non-periodic continuous broadband and white noise-like, it has natural concealment, and chaotic signal has ideal pseudo-random and related characteristics, which is especially suitable for secure communication applications

[4] Among them, chaotic image encryption has a very broad application prospect. In recent years, technologies such as holographic projection and holographic images have developed rapidly [11-13], but the relative privacy and data transmission requirements are higher. Therefore, the combination of holographic technology and chaotic secure communication is another worth exploring. field of.

references:

[1] Yu Simin. Chaotic System and Chaotic Circuit: Principle, Design and Application in Communication. Xi'an: Xidian University Press, 2011

[2] (United States) James Greck, translated by Zhang Shuyu. Chaos: Open up new science. Beijing: Higher Education Press, 2014

[3] Liu Zonghua. The basis of chaotic dynamics and its application in brain function. Beijing: Science Press, 2018

[4] Wang Xingyuan. Synchronization of chaotic systems and its application in secure communication. Beijing: Science Press, 2012

[5] Pecora L M, Carroll T L. Synchronization in chaotic systems． Physical Review Letters,1990,64(8):821-823

[6] Pham V T, Jafari S, Vaidyanathan S, et al. A novel memristive neural network with hiddenattractors and its circuitry implementation． Science China-Technological Sciences,2016,59(3):358-363

[7] Bao B C, Qian H, Wang J, et al. Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network. NonlinearDynamics, 2017, 90(4): 2359-2369

[8] Njitacke Z T, Kengne J. Complex dynamics of a 4D Hopfield neural networks (HNNs) with a nonlinear synaptic weight: Coexistence of multiple attractors and remerging Feigenbaumrees. AEU-International Journal of Electronics and Communications, 2018,93: 242-252

[9] Hu X Y, Liu C X, Liu L, et al. Chaotic dynamics in a neural network under electromagnetic radiation. Nonlinear Dynamics, 2018, 91(3): 1541-1554

[10] Chen C J, Chen J Q, Bao H, et al. Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons． NonlinearDynamics, 2019, 95(10): 3385-3399

[11] http://www.quanxiwang.com/news/show-5428.html

[12]https://baike.baidu.com/item/%E5%85%A8%E6%81%AF%E5%9B%BE%E5%83%8F/9554377?fr=aladdin

[13]https://baike.baidu.com/item/%E5%85%A8%E6%81%AF%E6%8A%95%E5%BD%B1/9443226?fr=aladdin