scholarly journals Interspike Interval Correlations, Memory, Adaptation, and Refractoriness in a Leaky Integrate-and-Fire Model with Threshold Fatigue

2003 ◽  
Vol 15 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Maurice J. Chacron ◽  
Khashayar Pakdaman ◽  
André Longtin
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Discharge Rate ◽  
Correlation Coefficients ◽  
Stimulus Onset ◽  
Constant Current ◽  
Integrate And Fire ◽  
Sinusoidal Currents ◽  
Lif Neuron ◽  
Sensitivity To Initial Conditions

Neuronal adaptation as well as interdischarge interval correlations have been shown to be functionally important properties of physiological neurons. We explore the dynamics of a modified leaky integrate-and-fire (LIF) neuron, referred to as the LIF with threshold fatigue, and show that it reproduces these properties. In this model, the postdischarge threshold reset depends on the preceding sequence of discharge times. We show that in response to various classes of stimuli, namely, constant currents, step currents, white gaussian noise, and sinusoidal currents, the model exhibits new behavior compared with the standard LIF neuron. More precisely, (1) step currents lead to adaptation, that is, a progressive decrease of the discharge rate following the stimulus onset, while in the standard LIF, no such patterns are possible; (2) a saturation in the firing rate occurs in certain regimes, a behavior not seen in the LIF neuron; (3) interspike intervals of the noise-driven modified LIF under constant current are correlated in a way reminiscent of experimental observations, while those of the standard LIF are independent of one another; (4) the magnitude of the correlation coefficients decreases as a function of noise intensity; and (5) the dynamics of the sinusoidally forced modified LIF are described by iterates of an annulus map, an extension to the circle map dynamics displayed by the LIF model. Under certain conditions, this map can give rise to sensitivity to initial conditions and thus chaotic behavior.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

A BIQUADRATIC SYSTEM OF TWO ORDER ONE DIFFERENCE EQUATIONS: PERIODS, CHAOTIC BEHAVIOR OF THE ASSOCIATED DYNAMICAL SYSTEM

2012 ◽  
Vol 22 (11) ◽  
pp. 1250266 ◽  
Author(s):  
GUY BASTIEN ◽  
MARC ROGALSKI
Keyword(s):  
Dynamical System ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Invariant Function ◽  
Minimal Period ◽  
Global Sensitivity ◽  
Open Set ◽  
Sensitivity To Initial Conditions

We study in [Formula: see text] the biquadratic system of two order one difference equations [Formula: see text] for some values of the parameters. We show that there is an invariant function G, and so that the orbit of a point (u0, v0) in some invariant open set U is on an invariant ellipse, and that the restriction on this ellipse of the associated dynamical system is conjugated to a rotation on a circle. The equilibrium is locally stable and the solutions (un, vn) are permanent. We show also that the starting points with periodic orbit are dense in U, and that every integer p ≥ N(a, b, c) is the minimal period of a periodic solution (un, vn). Moreover, the restriction of the dynamical system to the invariant compact "annulus" {K1 ≤ G ≤ K2} has global sensitivity to initial conditions, for inf U G < K1 < K2 < sup U G. Otherwise, outside U the solutions tend to infinity. At last we prove that the possible rational periodic solutions, when a, b, c are rational, may only be two or three-periodic, and we determine exactly the triples (a, b, c) for which such rational two or three-periodic solutions exist.

A Fractional-Order Hyperchaotic System and its Circuit Implement

2014 ◽  
Vol 701-702 ◽  
pp. 1143-1147
Author(s):  
Qi Li Wang
Keyword(s):  
Fractional Order ◽  
Strange Attractor ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Order System ◽  
Hyperchaotic System ◽  
Dynamical Properties ◽  
Simulation Results ◽  
Sensitivity To Initial Conditions

A fractional-order hyperchaotic system was proposed and some basic dynamical properties were investigated to show chaotic behavior. These properties include instability of equilibria, sensitivity to initial conditions, strange attractor, Lyapunov exponents, and bifurcation. The fractional-order system presents hyperchaos, chaos, and periodic behavior when the parameters vary continuously. Then, an analog circuit is designed onMultisim 11and the Multisim results are agreed with the simulation results.

Complex Response to Periodic Inhibition in Simple and Detailed Neuronal Models

1999 ◽  
Vol 11 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Corrado Bernasconi ◽  
Kaspar Schindler ◽  
Ruedi Stoop ◽  
Rodney Douglas
Keyword(s):  
Chaotic Behavior ◽  
Phase Locking ◽  
Neural Model ◽  
Realistic Model ◽  
Membrane Properties ◽  
Biophysical Model ◽  
Constant Current ◽  
Complex Response ◽  
Integrate And Fire ◽  
Neocortical Neurons

Constant current injection with superimposed periodic inhibition gives rise to phase locking as well as chaotic activity in rat neocortical neurons. Here we compare the behavior of a leaky integrate-and-fire neural model with that of a biophysically realistic model of the rat neuron to determine which membrane properties influence the response to such stimuli. We find that only the biophysical model with voltage-sensitive conductances can produce chaotic behavior.

A New Image Encryption Scheme Using Dual Chaotic Map Synchronization

2020 ◽  
Vol 18 (1) ◽  
Keyword(s):  
Image Encryption ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Chaotic Map ◽  
Security Applications ◽  
The Common ◽  
And Diffusion ◽  
Confusion And Diffusion ◽  
Sensitivity To Initial Conditions ◽  
Diffusion Properties

Chaotic systems behavior attracts many researchers in the field of image encryption. The major advantage of using chaos as the basis for developing a crypto-system is due to its sensitivity to initial conditions and parameter tunning as well as the random-like behavior which resembles the main ingredients of a good cipher namely the confusion and diffusion properties. In this article, we present a new scheme based on the synchronization of dual chaotic systems namely Lorenz and Chen chaotic systems and prove that those chaotic maps can be completely synchronized with other under suitable conditions and specific parameters that make a new addition to the chaotic based encryption systems. This addition provides a master-slave configuration that is utilized to construct the proposed dual synchronized chaos-based cipher scheme. The common security analyses are performed to validate the effectiveness of the proposed scheme. Based on all experiments and analyses, we can conclude that this scheme is secure, efficient, robust, reliable, and can be directly applied successfully for many practical security applications in insecure network channels such as the Internet

scholarly journals Nonlinear Behavior of a Magnetic Bearing System

1995 ◽  
Vol 117 (3) ◽  
pp. 582-588 ◽  
Author(s):  
L. N. Virgin ◽  
T. F. Walsh ◽  
J. D. Knight
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Nonlinear Behavior ◽  
Analytical Techniques ◽  
Magnetic Bearing ◽  
Forced Response ◽  
The Mathematical Model ◽  
Two Degree Of Freedom ◽  
Sensitivity To Initial Conditions ◽  
Bearing System

This paper describes the results of a study into the dynamic behavior of a magnetic bearing system. The research focuses attention on the influence of nonlinearities on the forced response of a two-degree-of-freedom rotating mass suspended by magnetic bearings and subject to rotating unbalance and feedback control. Geometric coupling between the degrees of freedom leads to a pair of nonlinear ordinary differential equations, which are then solved using both numerical simulation and approximate analytical techniques. The system exhibits a variety of interesting and somewhat unexpected phenomena including various amplitude driven bifurcational events, sensitivity to initial conditions, and the complete loss of stability associated with the escape from the potential well in which the system can be thought to be oscillating. An approximate criterion to avoid this last possibility is developed based on concepts of limiting the response of the system. The present paper may be considered as an extension to an earlier study by the same authors, which described the practical context of the work, free vibration, control aspects, and derivation of the mathematical model.

A High Rate, High Capacity and Long Life (LiFePO4+AC)/Li4Ti5O12 Hybrid Battery-Supercapacitor

2014 ◽  
Vol 936 ◽  
pp. 496-502
Author(s):  
Xue Bu Hu ◽  
Zi Ji Lin ◽  
Yong Long Zhang
Keyword(s):  
Leakage Current ◽  
Electrochemical Impedance ◽  
Discharge Rate ◽  
Performance Testing ◽  
High Energy ◽  
High Energy Density ◽  
Constant Current ◽  
Electrochemical Performances ◽  
Capacity Loss ◽  
Charge Discharge

A hybrid battery-supercapacitor (LiFePO4+AC)/Li4Ti5O12 using a Li4Ti5O12 anode and a LiFePO4/activated carbon (AC) composite cathode was built. The electrochemical performances of the hybrid battery-supercapacitor (LiFePO4+AC)/Li4Ti5O12 were characterized by constant current charge-discharge, rate charge-discharge, electrochemical impedance spectra, internal resistance, leakage current, self-discharge and cycle performance testing. The results show that (LiFePO4+AC)/Li4Ti5O12 hybrid battery-supercapacitors have rapid charge-discharge performance, high energy density, long cycle life, low resistance, low leakage current and self-discharge rate, which meet the requirements of practical power supply and can be applied in auxiliary power supplies for hybrid electric vehicles. At 4C rate, the capacity loss of (LiFePO4+AC)/Li4Ti5O12 hybrid battery-supercapacitors in constant current mode is no more than 7.71% after 2000 cycles, and the capacity loss in constant current-constant voltage mode is no more than 4.51% after 1500 cycles.

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

scholarly journals Climate Vibrations and Chaotic Behavior of Earth’s Inclination in the Laskar’s Model of a Moonless Earth

2019 ◽  
Vol 224 ◽  
pp. 03009
Author(s):  
Tatjana Gurina ◽  
Vyacheslav Salin
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Problem Parameter ◽  
System Of Differential Equations ◽  
Hamilton Function ◽  
Autonomous Hamiltonian System ◽  
The Earth ◽  
Time Period ◽  
Rotation Of The Earth ◽  
Regular Region

The model of the moonless Earth, introduced by J. Laskar, has the form of a non-autonomous Hamiltonian system of differential equations for two variables: the cosine of the angle of inclination and the longitude of the axis of rotation of the Earth. The system describes the rotational dynamics of the Earth under the influence of the sun and planets. Earth perturbations from other planets of the solar system are considered periodic and are taken into account using the first four terms of the Fourier expansion of the corresponding part of the Hamilton function with known amplitudes and frequencies. The initial inclination of the Earth is considered as a parameter of the problem. The system was numerically integrated over a time period of 18 million years for various values of the initial inclination from 0 to 180 degrees. Three chaotic gaps of the initial inclination were found. During the bifurcation study, singular points were found and special segments of the non-autonomous system were obtained. A bifurcation diagram of the system is constructed by the initial inclination parameter. Poincare cartographic maps are constructed. The system is written in variations on the initial conditions for the Laskar system, and with its help the dependences of the problem parameter of the senior Lyapunov exponent and the averaged MEGNO indicator are calculated. The results confirm the presence of three chaotic and one regular region of variation of the bifurcation parameter of the problem.

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