Related papers: Hash functions using chaotic iterations
We show that the statistics of a chaotic system can be predicted by constructing an associated sequence of periodic differential operators and computing their densities of states. For such operators, the density of states is well understood…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
There is one-to-one correspondence between quadratic operators (mapping $\mathbb R^m$ to itself) and cubic matrices. It is known that any quadratic operator corresponding to a stochastic (in a fixed sense) cubic matrix preserves the…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We present a new optoelectronic architecture intended for chaotic optical intensity generation. The principle relies on an electro-optic non-linear delay dynamics, which non linearity is performed by a 4-waves integrated optics…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
This paper discusses mixing of chaotic systems as a dependable method for secure communication. Distribution of the entropy function for steady state as well as plaintext input sequences are analyzed. It is shown that the mixing of chaotic…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
This is a draft paper, proving that the inversion process that occurs in DNA mutations, is indeed chaotic as it is defined by the Devaney's theory.
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
Neural network inference typically operates on raw input data, increasing the risk of exposure during preprocessing and inference. Moreover, neural architectures lack efficient built-in mechanisms for directly authenticating input data.…
In this paper, we study various chaos of topological group or semigroup actions.
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function…