Encontrados 22 documentos, a visualizar página 1 de 3
Synchronization and basins of Synchronized States in Two-Dimensional piecewise ...
Fournier-Prunaret, Daniele; Rocha, José; Caneco, Acilina; Fernandes, Sara; Grácio, ClaraThis paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on cou...
Symbolic Dynamics and chaotic synchronization
Gracio, Clara; Caneco, Acilina; Rocha, JoséChaotic communications schemes based on synchronization aim to provide security over the conventional communication schemes. Symbolic dynamics based on synchronization methods has provided high quality synchronization [5]. Symbolic dynamics is a rigorous way to investigate chaotic behavior with finite precision and can be used combined with information theory [13]. In previous works we have studied the kneading...
Geodesic length spectrum on compact Riemann surfaces
Gracio, Clara; Ramos, José SousaIn this paper we use techniques linking combinatorial structures (symbolic dynamics) and algebraic-geometric structures to study the variation of the geodesic length spectrum, with the Fenchel-Nielsen coordinates, which parametrize the surface of genus τ = 2. We explicitly compute length spectra, for all closed orientable hyperbolic genus two surfaces, identifying the exponential growth rate and the first terms...
Chaotic synchronization of Piecewise Linear Maps
Caneco, Acilina; Rocha, Jose; Gracio, ClaraWe derive a threshold value for the coupling strength in terms of the topological entropy, to achieve synchronization of two coupled piecewise linear maps, for the unidirectional and for the bidirectional coupling. We prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the bidirectional coupling of two identi...
Kneading theory analysis of the Duffing equation
Gracio, Clara; Caneco, Acilina; Rocha, JoséThe purpose of this paper is to study the symmetry effect on the kneading theory for symmetric unimodal maps and for symmetric bimodal maps. We obtain some properties about the kneading determinant for these maps, that implies some simplifications in the usual formula to compute, explicitly, the topological entropy. As an application, we study the chaotic behaviour of the two-well Duffing equation with forcing.
Topological entropy in the synchronization of piecewise linear and monotone map...
Gracio, Clara; Caneco, Acilina; Rocha, JoséIn this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated ...
Measuring complexity in a business cycle
Gracio, Clara; Januario, Cristina; Duarte, JorgeThe purpose of this paper is to study the dynamical behavior of a family of two- dimensional nonlinear maps associated to an economic model. Our objective is to measure the complexity of the system using techniques of symbolic dynamics in order to compute the topological entropy. The analysis of the variation of this im- portant topological invariant with the parameters of the system, allows us to distin- guish...
Measuring and controlling the chaotic motion of profits
Gracio, Clara; Januario, Cristina; Mendes, Diana; Duarte, JorgeThe study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in presence of chaos suggests the application of chaos control methods, w...
Chaotic synchronization of Piecewise Linear Maps
Gracio, Clara; Caneco, Acilina; Rocha, JoséWe derive a threshold value for the coupling strength in terms of the topological entropy, to achieve synchronization of two coupled piecewise linear maps, for the unidirectional and for the bidirectional coupling. We prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the bidirectional coupling of two identi...
Kneading theory analysis of the Duffing equation
Caneco, Acilina; Rocha, Jose; Gracio, ClaraThe purpose of this paper is to study the symmetry effect on the kneading theory for symmetric unimodal maps and for symmetric bimodal maps. We obtain some properties about the kneading determinant for these maps, that implies some simplifications in the usual formula to compute, explicitly, the topological entropy. As an application, we study the chaotic behaviour of the two-well Duffing equation with forcing.
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