The chaos in the synchrony of abnormal oscillations in a pair of neurons coupled via gap junction
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The synchrony of abnormally excitable neurons is a hallmark in epileptic seizure. In order to study the nonlinear oscillations in two neurons coupled via gap junction in epilepsy, the model of a pair of neurons is derived from Chay model that gives many kinds of abnormal oscillations in excitable neurons by three nonlinear variables dynamics equations. The synchrony between two electrically coupled excitable neurons is found and a theoretical effort is carried out to investigate the chaos in the synchronous oscillations of the membrane potentials by the Lyapunov exponent and the phase portrait. It is shown that synchronous abnormal oscillations of membrane potentials can occur when the coupling strength of gap junction is large enough and the concentration of Ca/sup 2/ ions does not synchronize while the membrane potentials are synchronous and the coupling mechanism is chaotic. It is concluded that the synchrony and the chaos make birth to the new oscillations while disorder process such as epileptic seizure. The theoretical analysis may be helpful to investigate the mechanism of synchrony and the relationship between abnormal oscillations and gap junctions from nonlinear oscillatory points of view.Keywords:
Phase portrait
Oscillation (cell signaling)
It is proved theoretically that two chaotic maps,which have the topological conjugation relationship,hold the same Lyapunov Exponent.The security is limited if only using the Lyapunov exponent as the description of cryptology characteristics of the chaotic map.By means of pseudo-random features of the chaotic sequence,the security of chaotic sequence is analyzed through the calculation of auto-correlation function and cross-correlation function combing with the Lyapunov exponent.
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Exponent
Random sequence
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Phase portrait
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Phonetic signals are considered from the viewpoint of nonlinear dynamics. Phase portraits of the signals are analyzed in embedding space, dimension and the largest Lyapunov exponent are estimated. It is shown that dimension of speech signals is low and the largest Lyapunov exponent is positive.
Phase portrait
Correlation dimension
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The bifurcation phase portraits and exact nonlinear wave solutions of the modified Konopelchenko-Dubrovsky (KD) equation are studied by using the bifurcation method. The bifurcation phase portraits of the modified KD equation are given when a>0 and a<0. When different combinations of the parameters a, b, k and n, eighteen new exact nonlinear wave solutions for the modified KD equation are obtained.
Phase portrait
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Phase portrait
Harmonic
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In this study, we attempt to test chaotic behavior of selected the variables and to determine chaotic relation between economic growth and coal consumption for the period from January, 1973 to March, 2018 in the USA by using Largest Lyapunov Exponents, Chaotic Causality perspectives. In this regard, firstly, it is aimed to identify nonlinear pattern of economic growth and coal consumption by BDS test. And secondly, it is purposed to determine chaotic behaviour of the analyzed series by Lyapunov Exponent. Further, chaotic causality is analyzed for this period. The analysis results demonstrate that coal consumption fluctuations have crucial effects on the USA’s economic growth in the long term.
Causality
Consumption
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Oscillatory regimes and bifurcation transitions in system with phase control are investigated. The bifurcation diagrams and phase portraits of the attractors are presented with various scenarios of evolution of the oscillatory motions versus the system parameters. New features of the system's chaotic behaviour are observed.
Phase portrait
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Based on the further evolvement of the improved chaotic system with constant Lyapunov exponent spectrum, by introducing an absolute term in the dynamic equation, a novel chaotic attractor is found in this paper. Firsty, the existence of chaotic attractor is verified by simulation of phase portrait, Poincaré mapping, and Lyapunov exponent spectrum. Secondly, the basic dynamical behaviour of the new system is investigated and expounded. Simulation of Lyapunov exponent spectrum, bifurcation diagram and numerical analysis on amplitude evolvement of state variables show that the state variables of the chaotic system can be modified linearly by a global linear amplitude adjuster while the Lyapunov exponent spectrum keeps on stable and the chaotic attractor displays the same phase portrait. Finally, an analog circuit is designed to implement the new system, the chaotic attractor is observed and the action of global linear amplitude adjuster is verified, all of which show a good agreement between numerical simulation and experimental results.
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Rössler attractor
Constant (computer programming)
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This paper is aim to build a monitoring method based on several chaotic characteristics,through chaotic characteristics analyzing of the acoustic emission signal from cutting tool and analyzing the trends of tool wear.Chaotic characteristics analyzed and described based on chaotic theory in different periods of acoustic emission signal from cutting tool,are including:(1) qualitative description,reconstructing the strange attractor track and Poincare map of the acoustic emission series;(2) quantitative description,computing correlation dimension and the max lyapunov exponent of the acoustic emission signal at different periods.Then chaotic characteristics computing result were analyzed by the least square method.The results show that chaotic phenomena exist in acoustic emission signal,and the correlation dimension and the max Lyapunov exponent have relationship with tool wear state.At last the paper provides a new idea for online monitoring and prediction of tool wear state.
Correlation dimension
Acoustic Emission
SIGNAL (programming language)
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This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.
Phase portrait
Equilibrium point
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