Largest Lyapunov Exponent Spectrum Research Articles

Fingerprint construction of optical transmitters based on the characteristic of electro-optic chaos for secure authentication.

In this paper, an optical transmitter authentication method using hardware fingerprints based on the characteristic of electro-optic chaos is proposed. By means of phase space reconstruction of chaotic time series generated by an electro-optic feedback loop, the largest Lyapunov exponent spectrum (LLES) is defined and used as the hardware fingerprint for secure authentication. The time division multiplexing (TDM) module and the optical temporal encryption (OTE) module are introduced to combine chaotic signal and the message to ensure the security of the fingerprint. Support vector machine (SVM) models are trained to recognize legal and illegal optical transmitters at the receiver. Simulation results show that LLES of chaos has the fingerprint characteristic and is highly sensitive to the time delay of the electro-optic feedback loop. The trained SVM models can distinguish electro-optic chaos generated by different feedback loops with a time delay difference of only 0.03ns and have a good anti-noise ability. Experimental results show that the recognition accuracy of the authentication module based on LLES can reach 98.20% for both legal and illegal transmitters. Our strategy can improve the defense ability of optical networks against active injection attacks and has high flexibility.

A Simple Parallel Chaotic Circuit Based on Memristor.

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

A Hénon-like map inspired by the generalized discrete-time FitzHugh–Nagumo model

The patterns of discharge activity are closely associated with the physiological manifestation of neurons, and hence, it is particularly significant to understand the dynamic behavior of the patterns. In this paper, a Henon-like map (generalized map) system is reported, which is derived from the discrete-time FitzHugh–Nagumo model that is a simplification of the classical Hodgkin–Huxley neuron model. Our main contributions are as follows: (i) proposing the Henon-like map; (ii) discovering the fractal structure and the chaos of the map; and (iii) presenting the horseshoe structure of the subsequence of the map. Specifically, it is observed that bifurcation structure in the process of period-doubling cascade to chaos is compatible with the largest Lyapunov exponent spectrum. Moreover, some basic properties of the generalized map are also analyzed with repeated numerical simulation, such as phase plane, bifurcation diagram, power spectrum and chaotic attractor. In addition, it is confirmed that the hidden horseshoe structure also exists in the generalized map. The potential connection between decomposition of chaotic behavior and period-3 is logically prospected. The behavior of period-doubling cascade to chaos and Smale horseshoe coexists in the map. Furthermore, the relationship between the internal mechanisms of the map and external performance may be discovered. Finally, the effects of forced external factors—delayed feedback, noise and electromagnetic field on the system—are evaluated. It may be the first time to study discrete neuron models by using Simulink simulation in the field of neurodynamics. In the above process, a circuit simulation is built in the Simulink package, which opens up a new path for the detection of discrete neuron network.

An Integer-Order Memristive System with Two- to Four-Scroll Chaotic Attractors and Its Fractional-Order Version with a Coexisting Chaotic Attractor

First, based on a linear passive capacitor C, a linear passive inductor L, an active-charge-controlled memristor, and a fourth-degree polynomial function determined by charge, an integer-order memristive system is suggested. The proposed integer-order memristive system can generate two-scroll, three-scroll, and four-scroll chaotic attractors. The complex dynamics behaviors are investigated numerically. The Lyapunov exponent spectrum with respect to linear passive inductor L and the two-scroll, three-scroll, and four-scroll chaotic attractors are yielded by numerical calculation. Second, based on the integer-order memristive chaotic system with a four-scroll attractor, a fractional-order version memristive system is suggested. The complex dynamics behaviors of its fractional-order version are studied numerically. The largest Lyapunov exponent spectrum with respect to fractional-order p is yielded. The coexisting two kinds of three-scroll chaotic attractors and the coexisting three-scroll and four-scroll chaotic attractors can be found in its fractional-order version.

A new three-dimensional chaotic system with wide range of parameters

A new three-dimensional chaotic system with large scope of parameters is proposed. Its properties such as equilibrium points, Poincaré map, the largest Lyapunov exponent spectra and bifurcation diagrams are analyzed theoretically and numerically. Theoretical analyses and simulation tests indicate that the proposed chaotic system can keep chaotic in a wide range of parameters. The system is recommendable for many engineering applications such as secure communications, cryptology, information processing, etc.

Nonlinear dynamic analysis of MPEG-4 video traffic

The main research motive is to analysis and to verify the inherent nonlinear character of MPEG-4 video. The power spectral density estimation of the video trafiic describes its 1/fβ and periodic characteristics. The principal components analysis of the reconstructed space dimension shows only several principal components can be the representation of all dimensions. The correlation dimension analysis proves its fractal characteristic. To accurately compute the largest Lyapunov exponent, the video traffic is divided into many parts. So the largest Lyapunov exponent spectrum is separately calculated using the small data sets method. The largest Lyapunov exponent spectrum shows there exists abundant nonlinear chaos in MPEG-4 video traffic. The conclusion can be made that MPEG-4 video traffic have complex nonlinear behavior and can be characterized by its power spectral density, principal components, correlation dimension and the largest Lyapunov exponent besides its common statistics.

COUPLED SYNCHRONIZATION OF HYPERCHAOTIC SYSTEMS

The hyperchaotic synchronization was achieved in LC oscillator via the mutual coupling method. The method to confirm coupling coefficient was given, the largest Lyapunov exponent spectra were calculated, and the connection between the coupling parameter and the synchronization time is discussed and given. Synchronization will be lost in the case of mismatched parameters.

Coupled synchronization of spatiotemporal chaos

The synchronization of spatiotemporal chaos is very important in secure communication. In this paper, we present an approach of nonlinear coupling to implement the synchronization of spatiotemporal chaos. Two cases are considered. The first is the same systems with same parameters; the second is the same systems with different parameters. And the largest Lyapunov exponent spectra are calculated. Our numerical simulation shows that the mutual coupling can induce generalized synchronization.

Control of Coupled Standard Map

In this work, we extend the periodic impulsive method to high-dimensional conservative system, and use the coupled standard map as an example to illustrate how to control the high-dimensional Hamiltonian chaos. When the periodic pulse is applied to one variable of the system, different periodic windows, quasiperiodic orbit and some special structure can be stabilized, even the approximate KAM curve. And the largest Lyapunov exponent spectra corresponding to different initial points are given.