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Intermittent Chaotic Neural Firing Characterized by Non-Smooth Features

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Chinese Physics Letters 2010年第7期27卷 47-50页

作者：王栋莫娟赵小燕古华光屈世显任维 College of Life Science Shaanxi Normal University Xi'an 710062 College of Physics and Information Technology Shaanxi Normal University Xi'an 710062

A chaotic firing pattern, characterized by non-smooth features and generated through the routine of intermittency from period 3, is observed in biological experiments on a neural firing pacemaker and reproduced in simulations by using a theoretical neuronal model with multiple time scales. This chaotic activity exhibits a scale law very similar to those of both the type-Ⅰ intermitteney generated in smooth systems and the type-Ⅴ intermittency in non-smooth systems.

关键词： chaos theory INTERMITTENCY (Nuclear physics) NEURONS MATHEMATICAL models NONLINEAR theories NUCLEAR physics TIME series analysis

Hyperchaos-chaos-Hyperchaos Transition in a Class of On-Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems

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Chinese Physics Letters 2008年第9期25卷 3169-3172页

作者：周茜陈增强袁祉 Department of Automation Nankai University Tianjin 300071

Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems＇ dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos.

关键词： NONLINEAR systems ATTRACTORS (Mathematics) chaos theory LORENZ equations BIFURCATION theory DYNAMICS QUANTUM chaos

Investigation of a Unified Chaotic System and Its Synchronization by Simulations

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Chinese Physics Letters 2010年第6期27卷 31-34页

作者： WU Qing-Chu FU Xin-Chu Michael Small Department of Mathematics Shanghai University Shanghai 200444 College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung Horn Kowloon Hong Kong

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.

关键词： chaos theory SYNCHRONIZATION SIMULATION methods & models FEEDBACK control systems NUMERICAL analysis LYAPUNOV exponents

Adaptive Function Projective Synchronization of Discrete Chaotic Systems with Unknown Parameters

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Chinese Physics Letters 2010年第5期27卷 33-35页

作者：吴召艳傅新楚 College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 Department of Mathematics Shanghai University Shanghai 200444

Adaptive function projective synchronization of discrete-time chaotic systems with unknown parameters is considered. Based on the contraction mapping theorem, proper controllers and estimators are designed. Illustrati... 详细信息

关键词： ADAPTIVE control systems SYNCHRONIZATION DISCRETE-time systems chaos theory MAPPINGS (Mathematics)

RESEARCH ON THE chaos DYNAMIC MODEL OF RUNOFF

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Journal of Hydrodynamics 2000年第2期12卷 85-91页

作者： Jiang, Chuanwen Quan, Xianzhang Zhang, Yongchuan Hou, Zhijian Huazhong Univ of Science and Technology Wuhan China

The identification of chaos in the study of runoff serial was introduced and a dynamic model of runoff with the observed values of runoff serial was proposed. By checking the difference between the original serial and substitute serial, the nature of the runoff serial can be identified. This paper thus provides an effective method for studying the rule of runoff. The study of the chaos features of runoff and the understanding of its nonlinear dynamic model are of great significance to the understanding of the rules of runoff movement and the accurate prediction.

关键词： chaos theory Dynamics Models Runoff

A Novel 2D Hyperchaotic with a Complex Dynamic Behavior for Color Image Encryption

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Computers, Materials & Continua 2023年第3期74卷 6555-6571页

作者： Yongsheng Hu Liyong Nan School of Information Engineering Binzhou UniversityBinzhou CityShandong Province256603China

The generation method of the key stream and the structure of the algorithm determine the security of the *** classical chaotic map has simple dynamic behavior and few control parameters,so it is not suitable for modern *** this paper,we design a new 2D hyperchaotic system called 2D simple structure and complex dynamic behavior map(2D-SSCDB).The 2D-SSCDB has a simple structure but has complex dynamic *** Lyapunov exponent verifies that the 2D-SSCDB has hyperchaotic behavior,and the parameter space in the hyperchaotic state is extensive and *** analysis and some randomness tests verify that the 2D-SSCDB can generate random sequences with good ***,to verify the excellent performance of the 2D-SSCDB,we use the 2D-SSCDB to generate a keystream for color image *** the encryption algorithm,the encryption algorithm scrambles and diffuses simultaneously,increasing the cryptographic system’s *** horizontal correlation,vertical correlation,and diagonal correlation of ciphertext are−0.0004,−0.0004 and 0.0007,*** average information entropy of the ciphertext is *** addition,the designed encryption algorithm reduces the correlation between the three channels of the color *** analysis shows that the color image encryption algorithm designed using 2DSSCDB has good security,can resist standard attack methods,and has high efficiency.

关键词： chaos theory 2D-SSCDB cryptography image encryption

Prediction Model of Weekly Retail Price for Eggs Based on Chaotic Neural Network

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Journal of Integrative Agriculture 2013年第12期12卷 2292-2299页

作者： LI Zhe-min CUI Li-guo XU Shi-wei WENG Ling-yun DONG Xiao-xia LI Gan-qiong YU Hai-peng Agricultural Information Institute Chinese Academy of Agricultural Sciences/Key Laboratory of Agri-Information Service TechnologyMinistry of Agriculture

This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in *** the process of determining the structure of the chaotic neural network,the number of input layer nodes of the network is calculated by reconstructing phase space and computing its saturated embedding dimension,and then the number of hidden layer nodes is estimated by trial and ***,this model is applied to predict the retail prices of eggs and compared with *** result shows that the chaotic neural network has better nonlinear fitting ability and higher precision in the prediction of weekly retail price of *** empirical result also shows that the chaotic neural network can be widely used in the field of short-term prediction of agricultural prices.

关键词： chaos theory chaotic neural network neural network technology short-term prediction weekly retail price of eggs

Finding chaos in Finnish GDP

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International Journal of Automation and computing 2014年第3期11卷 231-240页

作者： Radko Kíz Faculty of Electrical Engineering Czech Technical University

The goal of this paper is to analyze the Finnish gross domestic product(GDP) and to find chaos in the Finnish GDP. We chose Finland where data has been available since 1975, because we needed the longest time series possible. At first we estimated the time delay and the embedding dimension, which is needed for the Lyapunov exponent estimation and for the phase space ***, we computed the largest Lyapunov exponent, which is one of the important indicators of chaos. Then we calculated the 0-1 test for chaos. Finally we computed the Hurst exponent by rescaled range analysis and by dispersional analysis. The Hurst exponent is a numerical estimate of the predictability of a time series. In the end, we executed a recurrent analysis and displayed recurrence plots of detrended GDP time series. The results indicated that chaotic behaviors obviously exist in GDP.

关键词： chaos theory gross domestic product(GDP) time series analysis phase space reconstruction Hurst exponent largest Lyapunov exponent recurrent analysis.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

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Geoscience Frontiers 2022年第1期13卷 364-373页

作者： Guocheng Hao Juan Guo Wei Zhang Yunliang Chen David AYuen School of Mechanical Engineering and Electronic Information China University of GeosciencesWuhan 430074China School of Computer Science China University of GeosciencesWuhan 430074China Department of Mathematics Duke UniversityDurhamNC 27708USA Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and *** change tendency may be related to the occurrence of earthquake *** of the underlying intensity trend plays an important role in the analysis of data and disaster *** chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field *** main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field *** verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data *** to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function ***,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.

关键词： Earth’s natural pulse electromagnetic field chaos theory Radial Basis Function neural network Forecasting model