A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization

Abstract

Another chaotic nonlinear Lü model with complex factors is covered here. We can build this riotous complex system when we add a complex nonlinear term to the third condition of the complex Lü system and think of it as if every one of the factors is mind boggling or complex. This system in real adaptation is a 6-dimensional continuous autonomous chaotic system. Different types of chaotic complex Lü system are developed. Also, another sort of synchronization is presented by us which is simple for anybody to ponder for the chaotic complex nonlinear system. This sort might be called a complex antilag synchronization (CALS). There are irregular properties for CALS and they do not exist in the literature; for example, (i) the CALS contains or fused two sorts of synchronizations (antilag synchronization ALS and lag synchronization LS); (ii) in CALS the attractors of the main and slave systems are moving opposite or similar to each other with time lag; (iii) the state variable of the main system synchronizes with a different state variable of the slave system. A scheme is intended to accomplish CALS of chaotic complex systems in light of Lyapunov function. The acquired outcomes and effectiveness can be represented by a simulation case for our new model.

Dynamic Evolution Analysis of Stock Price Fluctuation and Its Control

“…From Remark 8, the fixedtime stable theorem of the dynamical system proposed in this paper achieves more faster convergence than the theorem proposed by Zuo and in [21,[24][25][26][27]]. Based on Lemma 6, we analyze the fixed-time control problem of system (11).…”

“…Although this assumption about (11) is flawed, (11) have the same properties as (10) for ( ) > 0. Therefore, we can deduce the part evolutionary behavior of the stock price fluctuation ( ) in practice by analyzing (11). Thus it can provide some theoretical reference for managers.…”

“…The various methods of chaos control have been put forward by researchers [11][12][13][14][15][16]; these control methods were mostly based on infinite time control. In fact, complex systems are usually required to be controlled in a certain amount of time, the finite time control became an important index to measure the quality of the control criteria, and it not only has important theoretical significance and also has important practical value [17].…”

A Novel Image Encryption Scheme Based on Self-Synchronous Chaotic Stream Cipher and Wavelet Transform

“…The parameters of MPE have embedding dimension m, delay factor τ, and scale factor s. For the choice of the parameter values of the multi-scale permutation entropy with the purpose of calculating the complexity of chaotic binary sequences, Sun et al [22] and Xu et al [23] give the recommended parameter range in order to obtain more accurate entropy values. On the basis of the theoretical research of the above references, in this experiment, we set m = 3, τ = 2, and s ∈ [3,7], respectively. The experimental results are shown in Table 1.…”

“…However, because of the high correlation and redundancy of adjacent pixels of the digital image, some international standard encryption algorithms are not suitable for image encryption, including 3DES (Triple Data Encryption Algorithm), IDEA (International Data Encryption Algorithm), and AES (Advanced Encryption Standard), etc. On the other hand, the chaotic nonlinear dynamic system has some good characteristics, such as positive Lyapunov exponents, ergodicity, sensitivity to initial conditions, topological transitivity, and unpredictability [2][3][4][5], and was widely applied in the field of cryptography and secret communication.…”