The subject of parameter estimation in linear signals embedded in white Gaussian noise has been extensively studied. The subject of nonlinear choatic signals, however, has received much less attention. This paper will examine some of the known techniques for estimating the parameters of chaotic signals such as iterative maps, including the tent map and the logistic map.

We consider a family of Markov maps on the unit interval, interpolating between the tent map and the Farey map. The latter map is not uniformly expanding. Each map being composed of two fractional linear transformations, the family generalizes many particular properties which for the case of the Farey map have been successfully exploited in number theory. We analyze the dynamics through the spe...

We investigate collective motion in high dimensional chaos, where all elements in a population behaves chaotically and incoherently in appearance. Numerical experiments for globally coupled tent maps show the existence of a quasi-periodic collective motion even under slight interaction. It is found that the amplitude of the collective motion F is scaled as, KF ∝ exp(−K−1), by the coupling stren...

We propose the deep-zoom analysis of composition logistic map and tent map, which are well-known discrete one-dimensional chaotic maps. The technique transforms each point a given orbit by removing first k-digits after decimal separator. found that pseudo-random qualities as number generator (PRNG) improve k parameter increases. This was evidenced fact it successfully passed randomness tests ev...

We test a Markov chain approximation to the segment description (Li, 2007) of chaos (and turbulence) on a tent map, the Minea system, the Hénon map, and the Lorenz system. For the tent map, we compute the probability transition matrix of the Markov chain on the segments for segment time length (iterations) T = 1, 2, 3, 100. The matrix has 1, 2, 4 tents corresponding to T = 1, 2, 3; and is almos...

We present an analog circuit implementation of the novel partial control method, that is able to sustain chaotic transient dynamics. The electronic circuit simulates the dynamics of the onedimensional slope-three tent map, for which the trajectories diverge to infinity for nearly all the initial conditions after behaving chaotically for a while. This is due to the existence of a nonattractive c...

Let T be a tent map with the slope strictly between √ 2 and 2. Suppose that the critical point of T is not recurrent. Let K denote the inverse limit space obtained by using T repeatedly as the bonding map. We prove that every homeomorphism of K to itself is isotopic to some power of the natural shift homeomorphism.

Secure exchange of sensitive information between different entities is a serious challenge in today’s environment. Therefore, various cryptosystems have been created specifically for this purpose. Various operations are used these cryptosystems. The most common substitution and permutation. substitution-box (S-box), look-up table that takes x bits as input replaces them with y bits, responsible...