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1.
By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking
properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the
parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting
features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence
of the escape parameter on the seed value and also on the initial phase of the perturbation etc. 相似文献
2.
Michael Nauenberg 《Journal of statistical physics》1987,47(3-4):459-475
The universal map for the period-doubling transition to chaos is studied numerically in the complex plane. The boundary of the domain of analyticity of this function is obtained graphically and is shown to be a fractal with self-similar properties obtained by rescaling with the universal constants and. In the complex parameter plane, this domain is shown asymptotically to be similar to part of the Mandelbrot set. 相似文献
3.
Narendra Singh 《Optics Communications》2009,282(6):1104-5407
We propose a new method for image encryption using Hartley transform with jigsaw transform and logistic map. Logistic map has been used to generate the random intensity mask which is known as chaotic random intensity mask. The problem of bare decryption with Hartley transform has been solved by using the jigsaw transform. In the proposed technique, the image is encrypted using two methods in which the second method is the extension of the first method. In the first method, the image is encrypted using Hartley transform and jigsaw transform. In the second method, the image is encrypted using Hartley transform, jigsaw transform and logistic map. The mean square errors and the signal to noise ratio have been calculated. Robustness of the technique in terms of blind decryption and the algorithmic complexity has been evaluated. The optical implementation has been proposed. The computer simulations are presented to verify the validity of the proposed technique. 相似文献
4.
We study the dynamical behavior of vehicular traffic through a series of traffic signals. The vehicular traffic is controlled with the use of the cycle time generated by a logistic map. Each signal changes periodically with a cycle time, and the cycle time varies from signal to signal. The nonlinear dynamic model of the vehicular motion is presented by a nonlinear map including the logistic map. The vehicular traffic exhibits very complex behavior on varying both the cycle time and the logistic-map parameter a. For a>3, the arrival time shows a linear dependence on the cycle time. Also, the dependence of vehicular motion on parameter a is clarified. 相似文献
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7.
Feng-guo Li 《Central European Journal of Physics》2008,6(3):539-545
Noise can induce an inverse period-doubling transition and chaos. The effects of noise on each periodic orbit of three different
period sequences are investigated for the logistic map. It is found that the dynamical behavior of each orbit, induced by
an uncorrelated Gaussian white noise, is different in the mergence transition. For an orbit of the period-six sequence, the
maximum of the probability density in the presence of noise is greater than that in the absence of noise. It is also found
that, under the same intensity of noise, the effects of uncorrelated Gaussian white noise and exponentially correlated colored
(Gaussian) noise on the period-four sequence are different.
相似文献
8.
The complex dynamics of the logistic map via two periodic impulsive forces is investigated in this paper. The influences of the system parameter and the impulsive forces on the dynamics of the system are studied respectively. With the parameter varying, the system produces the phenomenon such as periodic solutions, chaotic solutions, and chaotic crisis. Furthermore, the system can evolve to chaos by a cascading of period-doubling bifurcations. The Poincare′ map of the logistic map via two periodic impulsive forces is constructed and its bifurcation is analyzed. Finally, the Floquet theory is extended to explore the bifurcation mechanism for the periodic solutions of this non-smooth map. 相似文献
9.
10.
We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific
nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively
from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated
logistic map is less chaotic compared to the logistic map. 相似文献
11.
In this Letter, stability analysis is applied to a two-dimensional Logistic coupled map lattice with the periodic boundary conditions. The conditions of Turing instability are obtained, and various patterns can be exhibited by numerical simulations in the Turing instability region. For example, space-time periodic structures, periodic or quasiperiodic traveling wave solutions, stationary wave solutions, spiral waves, and spatiotemporal chaos, etc. have been observed. In particular, the different pattern structures have also been observed for same parameters and different initial values. That is, pattern structures also depend on the initial values. The similar patterns have also been seen in relevant references. However, the present Letter owes to pattern formation via diffusion-driven instabilities because the system is stable in the absence of diffusion. 相似文献
12.
The relation between chaotic behavior and complexity for one-dimensional maps is discussed. The one-dimensional maps are mapped
into a binary string via symbolic dynamics in order to evaluate the complexity. We apply the complexity measure of Lempel
and Ziv to these binary strings. To characterize the chaotic behavior, we calculate the Liapunov exponent. We show that the
exact normalized complexity for the logistic mapf: [0,1]→[0,1],f(x)=4x(1−x) is given by 1. 相似文献
13.
Natural systems are essentially nonlinear being neither completely ordered nor completely random. These nonlinearities are responsible for a great variety of possibilities that includes chaos. On this basis, the effect of randomness on chaos and order of nonlinear dynamical systems is an important feature to be understood. This Letter considers randomness as fluctuations and uncertainties due to noise and investigates its influence in the nonlinear dynamical behavior of coupled logistic maps. The noise effect is included by adding random variations either to parameters or to state variables. Besides, the coupling uncertainty is investigated by assuming tinny values for the connection parameters, representing the idea that all Nature is, in some sense, weakly connected. Results from numerical simulations show situations where noise alters the system nonlinear dynamics. 相似文献
14.
Makisha P.S. Maier 《Physics letters. A》2010,374(8):1028-3129
In ecological modeling, seasonality can be represented as a switching between different environmental conditions. This switching strategy can be related to the so-called Parrondian games, where the alternation of two losing games yield a winning game. Hence we can consider two dynamics that, by themselves, yield undesirable behaviors, but when alternated yield a desirable oscillatory behavior. In this case, we also consider a noisy switching strategy and find that the desirable oscillatory behavior prevails. 相似文献
15.
The movement of a particle could be depicted by the Mandelbrot set from the fractal viewpoint. According to the requirement, the movement of the particle needs to show different behaviors. In this paper, the feedback control method is taken on the classical Mandelbrot set. By amending the feedback item in the controller, the control method is applied to the generalized Mandelbrot set and by taking the reference item to be the trajectory of another system, the synchronization of Mandelbrot sets is achieved. 相似文献
16.
We analyze the q-deformed logistic map, where the q-deformation follows the scheme inspired in the Tsallis q-exponential function. We compute the topological entropy of the dynamical system, obtaining the parametric region in which the topological entropy is positive and hence the region in which chaos in the sense of Li and Yorke exists. In addition, it is shown the existence of the so-called Parrondo's paradox where two simple maps are combined to give a complicated dynamical behavior. 相似文献
17.
Y. Liu Z-Y. Sun L-J. An 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(4):481-484
Banded spherulite patterns are simulated in two dimensions by means of a
coupled logistic map lattice model. Both target pattern and spiral pattern
which have been proved to be existent experimentally in banded spherulite
are obtained by choosing suitable parameters in the model. The simulation
results also indicate that the band spacing is decreased with the increase
of parameter μ in the logistic map and increased with the increase of
the coupling parameter ε, which is quite similar to the results
in some experiments. Moreover, the relationship between the parameters and
the corresponding patterns is obtained, and the target patterns and spiral
patterns are distinguished for a given group of initial values, which may
guide the study of banded spherulite. 相似文献
18.
M. Napiórkowski 《Physics letters. A》1985,113(3):111-113
It is shown numerically that the one-dimensional logistic map displays at its periodic windows a generalized final state sensitivity with respect to initial conditions. The uncertainty exponent characterising this sensitivity is analysed at various values of the control parameter. 相似文献
19.
Takashi Nagatani 《Physics letters. A》2013,377(34-36):2047-2051
We study the dynamic behavior in the elevator traffic controlled by capacity when the inflow rate of passengers into elevators varies periodically with time. The dynamics of elevators is described by the piecewise map model combined with the circle map. The motion of the elevators depends on the inflow rate, its period, and the number of elevators. The motion in the piecewise map model combined with the circle map shows a complex behavior different from the motion in the piecewise map model. 相似文献
20.
The effect of using the output of one logistic map to modulate the accessible parameter of a second logistic map is examined. Rigorous analytical results provide some predictions on the effect of this type of modulation, and those effects are tested numerically. 相似文献