2,312 publications from this institution
A systematic methodology for generating multi-folded torus chaotic attractors from a simple three-dimensional piecewise-linear system is presented in this paper. Theoretical analysis shows that multi-folded torus chaotic attractors can be created via alternative switching between two piecewise-linear systems. A novel circuit diagram is designed for physically creating multi-folded torus chaotic attractors. This is the first time in the literature to experimentally verify a maximum 9-folded torus chaotic attractor that is generated by an analog circuit.
Recently two encryption schemes were proposed by combining circular bit shift and XOR operations, under the control of a pseudorandom bit sequence (PRBS) generated from a chaotic system. This Letter studies the security of these two encryption schemes and reports the following findings: (1) there exist some security defects in both schemes; (2) the underlying chaotic PRBS can be reconstructed as an equivalent key by using only two chosen plaintexts; (3) most elements in the underlying chaotic PRBS can be obtained by a differential known-plaintext attack using only two known plaintexts. Experimental results are given to demonstrate the feasibility of the proposed attack.
In the Letter, we propose a simple, yet general and mathematically rigorous bifurcation control method for bifurcation suppression in an abstract system setting that covers both continuous and discrete cases defined by nonlinear operators in Banach spaces.
Mobile robots can be divided into wheeled robots and legged robots. Wheeled robots have strong stability and low complexity, whereas legged robots have strong adaptability to terrain, both of them are the focus in the field of robotics research at present. With the deepening of research on mobile robots, the research focus has gradually shifted from mechanical structure design to improving the robot's adaptability to the external environment, that is, the ability to autonomously perceive and interact with the external environment. The perception of the external environment relies on sensors. Currently, the research on single sensor detection has been relatively mature, such as single visual SLAM and laser SLAM. However, how to fuse the information from the different sensors to improve the accuracy and stability of detection is still a research hotspot. In this paper, a fusion scheme of vision and laser SLAM (Simultaneous Localization and Mapping) is proposed to fuse the information of the above two sensors, and experiments are carried out on wheeled and legged robots respectively. Finally, the experimental results were compared and the possible optimization measures were proposed.
Recently four chaos-based image encryption schemes were proposed. Essentially, the four schemes can be classified into one class, which is composed of two basic parts: permutation of position and diffusion of pixel value with the same cipher-text feedback function. The operations involved in the two basic parts are determined by a pseudo random number sequence (PRNS) generated from iterating a chaotic dynamic system. According to the security requirement, the two basic parts are performed alternatively for some rounds. Although the designers claimed that the schemes are of high quality, we found the following security problems: 1) the schemes are not sensitive to the changes of plain-images; 2) the schemes are not sensitive to the changes of the key streams generated by any secret key; 3) there exists a serious flaw of the diffusion function; 4) the schemes can be broken with no more than dlogL(MN)e+3 chosen-images when the iteration number is equal to one, where MN is the size of the plain-image and L is the number of different pixel values; 5) the cryptanalysis on one scheme proposed by another research group is questionable.
This paper is concerned with the generation of multi-stripe chaotic attractors. Simple periodic nonlinear functions are employed to transform the original chaotic attractors to a pattern with multiple “parallel” or “rectangular” stripes. The relationship between the system parameters related to some periodic functions and the shape of the generated attractor is analyzed. Theoretic analysis about the underlying mechanism of generating the parallel stripes in the attractors is given. A general creation mechanism of multi-stripe attractors of the Lorenz system and other well-known chaotic systems is derived from the proposed unified approach.
No abstract is provided for this article.
In this Letter, we report the finding of period-adding scenarios with chaos in firing patterns, observed in biological experiments on a neural pacemaker, with fixed extra-cellular potassium concentration at different levels and taken extra-cellular calcium concentration as the bifurcation parameter. The experimental bifurcations in the two-dimensional parameter space demonstrate the existence of a chaotic region interwoven with the periodic region thereby forming a period-adding sequence with chaos. The behavior of the pacemaker in this region is qualitatively similar to that of the Hindmarsh–Rose neuron model in a well-known comb-shaped chaotic region in two-dimensional parameter spaces.
Many complex networks exhibit a scale-free vertex-degree distribution in a power-law form c k − γ , where k is the vertex-degree variable and c and γ are constants. To better understand the mechanism of power-law formation in real-world networks, it is effective to explore and analyze their vertex-degree sequences. We had shown before that, for a scale-free network of size N , if its vertex-degree sequence is k 1 < k 2 < ⋯ < k l , where { k 1 , k 2 , … , k l } is the set of all unequal vertex degrees in the network, and if its power exponent satisfies γ > 1 , then the length l of the vertex-degree sequence is of order log N . In the present paper, we further study complex networks with an exponential vertex-degree distribution and prove that the same conclusion also holds. In addition, we verify our claim by showing many real-world examples. We finally discuss some applications of the new finding in various fields of science and technology.
The purpose of our two-page communication was to study the computational complexity of a matrix inversion formula with the intention of showing its improvement over the naive method of computing the inverse separately. We did not intend to claim that the matrix inversion formula is our discovery. However, it is true that this point was not made clear in our short paper.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
In this note, discretization behaviors of the equivalent control based sliding-mode control (SMC) systems are studied. Some inherent dynamical properties of the discretized second-order systems are first explored. Upper bounds for the system steady states are established. The system's steady-state behaviors are discussed. The analysis for the second-order systems is then extended to higher order systems. Simulations are presented to verify the theoretical results.
This paper presents a design for a new fuzzy logic proportional-integral-derivative (PID) controller. The main motivation for this design was to control some known nonlinear systems, such as robotic manipulators, which violate the conventional assumption of the linear PID controller. This controller is developed by first describing the discrete-time linear PID control law and then progressively deriving the steps necessary to incorporate a fuzzy logic control mechanism into the modifications of the PID structure. The final version of this new fuzzy PID controller is a computationally efficient analytic scheme suitable for implementation in a real-time closed-loop digital control. Numerous computer simulations are included to demonstrate the effectiveness of the controller for both linear and nonlinear systems. Finally, a brief analysis is presented to prove that the controller has bounded-input/bounded-output (BIBO) stability.
Removing noisy links from an observed network is a task commonly required for preprocessing real-world network data. However, containing both noisy and clean links, the observed network cannot be treated as a trustworthy information source for supervised learning. Therefore, it is necessary but also technically challenging to detect noisy links in the context of data contamination. To address this issue, in the present article, a two-phased computational model is proposed, called link-information augmented twin autoencoders, which is able to deal with: 1) link information augmentation; 2) link-level contrastive denoising; 3) link information correction. Extensive experiments on six real-world networks verify that the proposed model outperforms other comparable methods in removing noisy links from the observed network so as to recover the real network from the corrupted one very accurately. Extended analyses also provide interpretable evidence to support the superiority of the proposed model for the task of network denoising.
As a powerful cryptanalysis tool, the method of return-map attacks can be used to extract secret messages masked by chaos in secure communication schemes. Recently, a simple defensive mechanism was presented to enhance the security of chaotic parameter modulation schemes against return-map attacks. Two techniques are combined in the proposed defensive mechanism: multistep parameter modulation and alternative driving of two different transmitter variables. This paper re-studies the security of this proposed defensive mechanism against return-map attacks, and points out that the security was much over-estimated in the original publication for both ciphertext-only attack and known/chosen-plaintext attacks. It is found that a deterministic relationship exists between the shape of the return map and the modulated parameter, and that such a relationship can be used to dramatically enhance return-map attacks thereby making them quite easy to break the defensive mechanism.
In this paper, we consider a nonlinear controlled system forced by stochastic disturbances. The problem addressed is to design a feedback regulator that can stabilize an equilibrium of the closed-loop system and, around this equilibrium, to synthesize a required dispersion of random states of the corresponding system. We use a stochastic sensitivity function technique to approximate the stationary probabilistic distribution of these random states. We also develop a new method for stabilization based on the stochastic sensitivity synthesis. A constructive description of the attainability set of the stochastic sensitivity matrices for a 3D system is given. The effectiveness of the new approach is demonstrated by the 3D stochastic Chen system. It is shown that the new regulator provides a low level of sensitivity and can suppress both regular and chaotic oscillations.
This paper proves that a binary operation ${\star}$ on ${[0, 1]}$, ensuring that the binary operation ${\curlywedge}$ is a ${t}$-norm or ${\curlyvee}$ is a ${t}$-conorm, is a ${t}$-norm, where ${\curlywedge}$ and ${\curlyvee}$ are special convolution operations defined by $${(f\curlywedge g)(x)=\sup\left\{f(y)\star g(z): y\vartriangle z=x\right\},} $$ $${(f\curlyvee g)(x)=\sup\left\{f(y)\star g(z): y\ \triangledown\ z=x\right\},} $$ for any ${f, g\in Map([0, 1], [0, 1])}$, where ${\vartriangle}$ and ${\triangledown}$ are a continuous ${t}$-norm and a continuous ${t}$-conorm on ${[0, 1]}$, answering negatively an open problem posed in \cite{HCT2015}. Besides, some characteristics of ${t}$-norm and ${t}$-conorm are obtained in terms of the binary operations ${\curlywedge}$ and ${\curlyvee}$.
