26,616 research outputs found
A multi-step differential transform method and application to non-chaotic or chaotic systems
International audienceThe differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi- step DTM, classical DTM and the classical Runge-Kutta method is presented. The results demonstrate reliability and efficiency of the algorithm developed
Chaotic multi-objective optimization based design of fractional order PI{\lambda}D{\mu} controller in AVR system
In this paper, a fractional order (FO) PI{\lambda}D\mu controller is designed
to take care of various contradictory objective functions for an Automatic
Voltage Regulator (AVR) system. An improved evolutionary Non-dominated Sorting
Genetic Algorithm II (NSGA II), which is augmented with a chaotic map for
greater effectiveness, is used for the multi-objective optimization problem.
The Pareto fronts showing the trade-off between different design criteria are
obtained for the PI{\lambda}D\mu and PID controller. A comparative analysis is
done with respect to the standard PID controller to demonstrate the merits and
demerits of the fractional order PI{\lambda}D\mu controller.Comment: 30 pages, 14 figure
How single neuron properties shape chaotic dynamics and signal transmission in random neural networks
While most models of randomly connected networks assume nodes with simple
dynamics, nodes in realistic highly connected networks, such as neurons in the
brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the
dynamical properties of nodes (such as single neurons) and recurrent
connections interact to shape the effective dynamics in large randomly
connected networks. A novel dynamical mean-field theory for strongly connected
networks of multi-dimensional rate units shows that the power spectrum of the
network activity in the chaotic phase emerges from a nonlinear sharpening of
the frequency response function of single units. For the case of
two-dimensional rate units with strong adaptation, we find that the network
exhibits a state of "resonant chaos", characterized by robust, narrow-band
stochastic oscillations. The coherence of stochastic oscillations is maximal at
the onset of chaos and their correlation time scales with the adaptation
timescale of single units. Surprisingly, the resonance frequency can be
predicted from the properties of isolated units, even in the presence of
heterogeneity in the adaptation parameters. In the presence of these
internally-generated chaotic fluctuations, the transmission of weak,
low-frequency signals is strongly enhanced by adaptation, whereas signal
transmission is not influenced by adaptation in the non-chaotic regime. Our
theoretical framework can be applied to other mechanisms at the level of single
nodes, such as synaptic filtering, refractoriness or spike synchronization.
These results advance our understanding of the interaction between the dynamics
of single units and recurrent connectivity, which is a fundamental step toward
the description of biologically realistic network models in the brain, or, more
generally, networks of other physical or man-made complex dynamical units
Image Encryption Based on Diffusion and Multiple Chaotic Maps
In the recent world, security is a prime important issue, and encryption is
one of the best alternative way to ensure security. More over, there are many
image encryption schemes have been proposed, each one of them has its own
strength and weakness. This paper presents a new algorithm for the image
encryption/decryption scheme. This paper is devoted to provide a secured image
encryption technique using multiple chaotic based circular mapping. In this
paper, first, a pair of sub keys is given by using chaotic logistic maps.
Second, the image is encrypted using logistic map sub key and in its
transformation leads to diffusion process. Third, sub keys are generated by
four different chaotic maps. Based on the initial conditions, each map may
produce various random numbers from various orbits of the maps. Among those
random numbers, a particular number and from a particular orbit are selected as
a key for the encryption algorithm. Based on the key, a binary sequence is
generated to control the encryption algorithm. The input image of 2-D is
transformed into a 1- D array by using two different scanning pattern (raster
and Zigzag) and then divided into various sub blocks. Then the position
permutation and value permutation is applied to each binary matrix based on
multiple chaos maps. Finally the receiver uses the same sub keys to decrypt the
encrypted images. The salient features of the proposed image encryption method
are loss-less, good peak signal-to-noise ratio (PSNR), Symmetric key
encryption, less cross correlation, very large number of secret keys, and
key-dependent pixel value replacement.Comment: 14 pages,9 figures and 5 tables;
http://airccse.org/journal/jnsa11_current.html, 201
LP-VIcode: a program to compute a suite of variational chaos indicators
An important point in analysing the dynamics of a given stellar or planetary
system is the reliable identification of the chaotic or regular behaviour of
its orbits. We introduce here the program LP-VIcode, a fully operational code
which efficiently computes a suite of ten variational chaos indicators for
dynamical systems in any number of dimensions. The user may choose to
simultaneously compute any number of chaos indicators among the following: the
Lyapunov Exponents, the Mean Exponential Growth factor of Nearby Orbits, the
Slope Estimation of the largest Lyapunov Characteristic Exponent, the Smaller
ALignment Index, the Generalized ALignment Index, the Fast Lyapunov Indicator,
the Othogonal Fast Lyapunov Indicator, the dynamical Spectra of Stretching
Numbers, the Spectral Distance, and the Relative Lyapunov Indicator. They are
combined in an efficient way, allowing the sharing of differential equations
whenever this is possible, and the individual stopping of their computation
when any of them saturates.Comment: 26 pages, 9 black-and-white figures. Accepted for publication in
Astronomy and Computing (Elsevier
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