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Synchronization and basins of Synchronized States in Two-Dimensional piecewise ...

Fournier-Prunaret, Daniele; Rocha, José; Caneco, Acilina; Fernandes, Sara; Grácio, Clara

This 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, José

Chaotic 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...


Chaotic synchronization of Piecewise Linear Maps

Caneco, Acilina; Rocha, Jose; Gracio, Clara

We 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, José

The 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, José

In 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 ...


Chaotic synchronization of Piecewise Linear Maps

Gracio, Clara; Caneco, Acilina; Rocha, José

We 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, Clara

The 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...

Caneco, Acilina; Rocha, Jose; Gracio, Clara

In 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 ...


Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators

Gracio, Clara; Caneco, Acilina; Rocha, José

In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincar´e cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for...


Symbolic Dynamics and Chaotic Synchronization in Coupled Duffing Oscillators

Caneco, Acilina; Gracio, Clara; Rocha, Jose

In this work we discuss the complete synchronization of two identical double-well Duffing oscillators unidirectionally coupled, from the point of view of symbolic dynamics. Working with Poincar´e cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized. We obtained analytically the threshold value of the coupling parameter for ...


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