Fractal Interpolation in Creating Prefractal Images
Generation of Quasi-Moiré Patterns: Fractality and Percolation
Integral manifolds of the N-body problem.
Inverse Limits, Economics, and Backward Dynamics.
We survey recent papers on the problem of backward dynamics in economics, providing along the way a glimpse at the economics perspective, a discussion of the economic models and mathematical tools involved, and a list of applicable literature in both mathematics and economics.
Linear bifurcation analysis with applications to relative socio-spatial dynamics.
Modular dynamical systems on networks
We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations,...
Nonautonomous dynamical systems and associated fields. (Systèmes dynamiques nonautonomous et des champs associés.)
Nonlinearity in social dynamics -- order versus chaos.
On energy conservation of the simplified Takahashi-Imada method
In long-time numerical integration of Hamiltonian systems, and especially in molecular dynamics simulation, it is important that the energy is well conserved. For symplectic integrators applied with sufficiently small step size, this is guaranteed by the existence of a modified Hamiltonian that is exactly conserved up to exponentially small terms. This article is concerned with the simplified Takahashi-Imada method, which is a modification of the Störmer-Verlet method that is as easy to implement...
On quantum twist maps and spectral properties of Floquet operators
On the anti–synchronization detection for the generalized Lorenz system and its applications to secure encryption
In this paper, a modified version of the Chaos Shift Keying (CSK) scheme for secure encryption and decryption of data will be discussed. The classical CSK method determines the correct value of binary signal through checking which initially unsynchronized system is getting synchronized. On the contrary, the new anti-synchronization CSK (ACSK) scheme determines the wrong value of binary signal through checking which already synchronized system is loosing synchronization. The ACSK scheme is implemented...
Period doubling bifurcations in a two-box model of the Brusselator
Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
Proposition de structures géométriques «amplifiées» pour le traitement des systèmes de points matériels
Redundancy relations for fault diagnosis in nonlinear uncertain systems
The problem of fault detection and isolation in nonlinear uncertain systems is studied within the scope of the analytical redundancy concept. The problem solution involves checking the redundancy relations existing among measured system inputs and outputs. A novel method is proposed for constructing redundancy relations based on system models described by differential equations whose right-hand sides are polynomials. The method involves a nonlinear transformation of the initial system model into...
Secure communications based on discrete time chaotic systems
Self-organization in interface dynamics and urban development.
Self-organized criticality and urban development.
Spectral properties of weakly almost periodic cosine functions
The spectral structure of the infinitesimal generator of a strongly continuous cosine function of linear bounded operators is investigated, under assumptions on the almost periodic behaviour of applications generated, in various ways, by C. Moreover, a first approach is presented to the analysis of connection between cosine functions and dynamical systems.
Spreadability, Vulnerability and Protector Control
In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: Spreadability, vulnerability and protector control. These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution
Symmetry in Architecture