We consider a family of piecewise linear bimodal maps having the outermost slopes positive and less than one. Three types of bifurcation structures incorporated into the parameter space of the map are described. These structures are formed by periodicity regions related to attracting cycles, namely, the skew tent map structure is associated with periodic points on two adjacent branches of the m...

We investigate the topological zeta function for unimodal maps in general and dynamical zeta functions for the tent map in particular. For the generic situation, when the kneading sequence is aperiodic, it is shown that the zeta functions have a natural boundary along its radius of convergence, beyond which the function lacks analytic continuation. We make a detailed study of the function ∏∞ n=...

The intriguing characteristics of chaotic maps have prompted researchers to use these sequences in watermarking systems to good effect. In this paper we aim to use a tent map to encrypt the binary logo to achieve a like-noise signal. This approach makes extraction of the watermark signal by potential attacker very hard. Embedding locations are selected based on certain principles. Experimental ...

Using the Perron-Frobenius operator we establish a new functional central limit theorem result for non-invertible measure preserving maps that are not necessarily ergodic. We apply the result to asymptotically periodic transformations and give an extensive specific example using the tent map.

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...

where β = β(β−1)−1, M ∈ N∪{∞}, and l0, l1, . . . is a uniquely determined (finite or infinite) sequence of non-negative integers (cf. [2]). Analogously to other types of expansions we may ask for bases β such that the set of numbers with periodic or even finite representation is as large as possible. In particular, we say that Tβ satisfies the periodicity property (P) if the orbit (T β (x))n≥1 ...

Based on the analysis of the properties of tent map, parallel chaos optimization algorithm (PCOA) using logistic map and outlook algorithm, a hybrid global optimization algorithm (PCOOA) is presented. The algorithm is structured in two stages. The first stage uses parallel chaos optimization based on tent map for global search, while outlook algorithm is employed in the second stage for local s...

He was employed at his ordinary duties up to the time of his death, and had never complained of any illness whatever during his four mouths service. Nor did enquiry elicit any knowledge of his having suffered from any disease on the part of his relations. At 7 A.M., on the morning of February the 9th, the Havildar in charge of a section of the Yak Corps gave some orders to Purba Nowgali who at ...