scholarly journals Complex anti-synchronization of two indistinguishable chaotic complex nonlinear models

2019 ◽  
Vol 52 (7-8) ◽  
pp. 922-928 ◽  
Author(s):  
Emad E Mahmoud ◽  
Madeha A Al-Adwani
Keyword(s):  
Lyapunov Function ◽  
Imaginary Part ◽  
Nonlinear Models ◽  
Chaotic Attractors ◽  
Complete Synchronization ◽  
The Real ◽  
State Variable ◽  
Phase Errors ◽  
Variable Modulus ◽  
Standard Framework

The principal target of this work is to introduce and examine a novel kind of complex synchronization. This sort may be called complex anti-synchronization. There are surprising properties of complex anti-synchronization that do not exist in the writing, for example, (1) this sort of synchronization can dissect just for complex nonlinear frameworks. (2) The complex anti-synchronization contains or connects two sorts of synchronizations (anti-synchronization and complete synchronization). Anti-synchronization happens between the real part of main framework and the imaginary part of the slave framework, although complete synchronization accomplishes between the real part of slave framework and the imaginary part of the main framework. (3) In complex anti-synchronization, the attractors of the essential and slave structures are moving symmetrical to each other with a similar structure. (4) The state variable of the standard framework synchronizes with an other state variable of the slave structure. An explanation of complex anti-synchronization is presented for two indistinguishable chaotic complex nonlinear frameworks. In view of the Lyapunov function, a plan is intended to accomplish complex anti-synchronization of disordered or chaotic attractors of these frameworks. The effectiveness of the obtained results is outlined by a reenactment illustration. Numerical outcomes are plotted to show state variable, modulus errors, phase errors and the development of the attractors of these chaotic frameworks after synchronization to demonstrate that complex anti-synchronization is accomplished.

Complex lag synchronization of two identical chaotic complex nonlinear systems

Open Physics ◽  
2014 ◽  
Vol 12 (1) ◽  
Author(s):  
Emad Mahmoud ◽  
Kholod Abualnaja
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Chaotic Attractors ◽  
State Variables ◽  
Lag Synchronization ◽  
Phase Errors ◽  
New Type ◽  
Complex Nonlinear Systems ◽  
Definition Of ◽  
Made In

AbstractMuch progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modulus errors and phase errors of these chaotic attractors after synchronization to prove that CLS is achieved.

Self-time-delay synchronization of time-delay coupled complex chaotic system and its applications to communication

2014 ◽  
Vol 25 (03) ◽  
pp. 1350102 ◽  
Author(s):  
Fangfang Zhang ◽  
Shutang Liu
Keyword(s):  
Time Delay ◽  
Imaginary Part ◽  
Speech Signal ◽  
Chaotic Systems ◽  
Time Lag ◽  
Control Technique ◽  
Complex State ◽  
The Real ◽  
State Variable ◽  
Complex Chaotic Systems

Considering the time lag produced by the transmission in chaos-communication, we present self-time-delay synchronization (STDS) of complex chaotic systems. STDS implies that the synchronization between the time-delay system (the receiver) and the original system (the transmitter) while maintaining the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. It is more suitable to simulate real communication situation. Aimed to time-delay coupled complex chaotic systems, the control law is derived by active control technique. Based on STDS, a novel communication scheme is further designed according to chaotic masking. In simulation, we take time-delay coupled complex Lorenz system transmitting actual speech signal (analog signal) and binary signal as examples. The speech signal contains two components, which are transmitted by the real part and imaginary part of one complex state variable. Two sequences of binary bits are converted into analog signals by 2M-ary and zero-order holder, then added into the real part and imaginary part of one complex state variable. Therefore, the STDS controller is realized by one critical state variable. It is simple in principle and easy to implement in engineering. Moreover, the communication system is robust to noise. It is possible to adopt cheap circuits with time-delay, which is economical and practical for communication.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

scholarly journals Design of delayed fractional state variable filter for parameter estimation of fractional nonlinear models

2018 ◽  
Vol 94 (4) ◽  
pp. 2697-2713 ◽  
Author(s):  
Walid Allafi ◽  
Ivan Zajic ◽  
Kotub Uddin ◽  
Zhonghua Shen ◽  
James Marco ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Models ◽  
State Variable ◽  
State Variable Filter

scholarly journals Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

Information ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 5 ◽  
Author(s):  
Liu ◽  
Mahmood ◽  
Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Membership Degree ◽  
The Real ◽  
Complex Valued

In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

One Method to Construct the S-Box Based on Improved Chaos Map

2014 ◽  
Vol 651-653 ◽  
pp. 2164-2167
Author(s):  
Hang Zhang ◽  
Xiao Jun Tong
Keyword(s):  
Imaginary Part ◽  
Logistic Map ◽  
Block Ciphers ◽  
Mandelbrot Set ◽  
New Method ◽  
Hénon Map ◽  
Henon Map ◽  
The Real

Many methods of constructing S-box often adopt the classical chaotic equations. Yet study found that some of the chaotic equations exists drawbacks. Based on that, this paper proposed a new method to generate S-Box by improving the Logistic map and Henon map, and combining the real and imaginary part of complex produced by the Mandelbrot set. By comparing with several other S-boxes proposed previously, the results show the S-box here has better cryptographic properties. So it has a good application prospect in block ciphers.

scholarly journals GAP EQUATION IN SCALAR FIELD THEORY AT FINITE TEMPERATURE

1999 ◽  
Vol 14 (04) ◽  
pp. 257-266
Author(s):  
KRISHNENDU MUKHERJEE
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Scalar Field ◽  
Imaginary Part ◽  
Finite Temperature ◽  
Thermal Mass ◽  
Scalar Field Theory ◽  
Gap Equation ◽  
The Real

We investigate the two-loop gap equation for the thermal mass of hot massless g2ϕ4 theory and find that the gap equation itself has a nonzero finite imaginary part. This implies that it is not possible to find the real thermal mass as a solution of the gap equation beyond g2 order in perturbation theory. We have solved the gap equation and obtained the real and imaginary parts of the thermal mass which are correct up to g4 order in perturbation theory.

FACE REPRESENTATION WITH GRADIENT ORIENTATIONS AND EULER MAPPING: APPLICATION TO FACE RECOGNITION

2014 ◽  
Vol 28 (08) ◽  
pp. 1456014 ◽  
Author(s):  
ZHAOKUI LI ◽  
LIXIN DING ◽  
YAN WANG ◽  
JINRONG HE
Keyword(s):  
Face Recognition ◽  
Imaginary Part ◽  
Feature Vector ◽  
Low Frequency ◽  
Subspace Learning ◽  
The Real ◽  
Face Representation ◽  
Central Pixel ◽  
Low Dimensional ◽  
Two Stages

This paper proposes a simple, yet very powerful local face representation, called the Gradient Orientations and Euler Mapping (GOEM). GOEM consists of two stages: gradient orientations and Euler mapping. In the first stage, we calculate gradient orientations of a central pixel and get the corresponding orientation representations by performing convolution operator. These representation results display spatial locality and orientation properties. To encompass different spatial localities and orientations, we concatenate all these representation results and derive a concatenated orientation feature vector. In the second stage, we define an explicit Euler mapping which maps the space of the concatenated orientation into a complex space. For a mapping image, we find that the imaginary part and the real part characterize the high frequency and the low frequency components, respectively. To encompass different frequencies, we concatenate the imaginary part and the real part and derive a concatenated mapping feature vector. For a given image, we use the two stages to construct a GOEM image and derive an augmented feature vector which resides in a space of very high dimensionality. In order to derive low-dimensional feature vector, we present a class of GOEM-based kernel subspace learning methods for face recognition. These methods, which are robust to changes in occlusion and illumination, apply the kernel subspace learning model with explicit Euler mapping to an augmented feature vector derived from the GOEM representation of face images. Experimental results show that our methods significantly outperform popular methods and achieve state-of-the-art performance for difficult problems such as illumination and occlusion-robust face recognition.

scholarly journals Stiffness of sphere–plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

2015 ◽  
Vol 6 ◽  
pp. 845-856 ◽  
Author(s):  
Jana Vlachová ◽  
Rebekka König ◽  
Diethelm Johannsmann
Keyword(s):  
Imaginary Part ◽  
Coulomb Friction ◽  
Ambient Medium ◽  
Normal Load ◽  
Contact Stiffness ◽  
Oscillation Amplitude ◽  
Partial Slip ◽  
Squeeze Flow ◽  
Frictional Stress ◽  
The Real

The stiffness of micron-sized sphere–plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0–20 nm). The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM), where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate) (PMMA). The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson–Kendall–Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo–Mindlin model. This finding is remarkable insofar, as the Cattaneo–Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor), which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip.

SAVVIDY VACUUM IN SU(2) YANG–MILLS THEORY

2005 ◽  
Vol 20 (22) ◽  
pp. 1655-1662 ◽  
Author(s):  
DANIEL KAY ◽  
A. KUMAR ◽  
R. PARTHASARATHY
Keyword(s):  
Energy Density ◽  
Imaginary Part ◽  
Functional Integral ◽  
Quadratic Approximation ◽  
Effective Energy ◽  
The Real ◽  
Yang Mills ◽  
The One

The one-loop effective energy density of a pure SU (2) Yang–Mills theory in the Savvidy background is reconsidered. The stable and the unstable modes are identified. The stable modes are treated in the quadratic approximation. For the unstable modes, the full expansion including the cubic and the quartic terms in the fluctuations is used. The functional integral for the unstable modes is evaluated and added to the result for the stable modes. The resulting energy density coincides with the real part in the quadratic approximation of earlier studies and there is now no imaginary part.

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