Basic geometrical and topological features are described for discontinuous systems modelling power converters. The global Poincaré map considered arises naturally from the sampling process in the oscillatory forced system. It is shown that this map belongs to the class of two-dimensional invertible continuous but only piecewise-smooth maps. It also contains a singular point at which critical cu...

We study, numerically and analytically, the singular limit of a vanishing flowing layer in tumbled granular flows in quasi-two-dimensional rotating containers. The limiting behavior is found to be identical under the two versions of the kinematic continuum model of such flows, and the transition to the limiting dynamics is analyzed in detail. In particular, we formulate the no-shear-layer dynam...

Abstract— In this paper, we provide possible vulnerabilities of the algorithm set forth by Mohamed Amin et al. [Commun. Nonlinear Sci. Numer. Simulat. 15, 3484-97, (2010)]. They proposed a block cipher algorithm using chaotic Tent map. For the Feistel structure used there are a certain vulnerabilities that can be exploited to find out the rotations the plaintext goes through. For a small number...

The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local unit possesses about the collective dynamics. Applications to locally and globally coupled map systems are considered. The prediction error exhibits phase tra...

This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system and the compressed measurement is obtained by downsampling the system output. The reconstruction is realized through the estimation of the excitation coeffici...

This paper presents a unified model, consisting of a linear dynamic system and a bounded static nonlinear operator. Most discrete-time chaotic systems, such as chaotic neural networks, Chua’s circuits, and Hénon map etc, can be transformed into this unified model. Based on the H∞ performance analysis of the estimation error system between the unified model and its improved Luenberger-like filte...

A vector field is piecewise smooth if its value jumps across a hypersurface, and a two-fold singularity is a point where the flow is tangent to the hypersurface from both sides. Two-folds are generic in piecewise smooth systems of three or more dimensions. We derive the local dynamics of all possible two-folds in three dimensions, including nonlinear effects around certain bifurcations, finding...

Parry showed that every continuous transitive piecewise monotonic map τ of the interval is conjugate (by an order preserving homeomorphism) to a uniformly piecewise linear map T (i.e., one with slopes ±s). In the current article, it is shown that the map T is unique. This is proven by showing that any order-preserving conjugacy between two continuous transitive uniformly piecewise linear maps i...

Experiments and theory characterize the novel chaotic neoclassical transport scaling as νcB in contrast to traditional collisional neoclassical transport scaling as ν 1/2 c B−1/2. This chaotic transport occurs when local trapping separatrices have θ-variations or temporal fluctuations. Experiments observe bulk particle transport, damping of Langmuir waves and diocotron waves, and nonlinear wave...

Particle Swarm Optimization (PSO) approach intertwined with Lozi map chaotic sequences to obtain Takagi–Sugeno (TS) fuzzy model for representing dynamical behaviours are proposed in this paper. The proposed method is an alternative for nonlinear identification approaches especially when dealing with complex systems that cannot always be modelled using first principles to determine their dynamic...