Intermittent Synchronization in a Pair of Coupled Chaotic Pendula

2) d The possibility that coupling between chaotic system or subsystems could result in synchronization of the d namics was introduced by Pecora and Carroll [1]. A co siderable body of theoretical work has now emerged this general topic, the investigations focusing on a num ber of prototype systems including Rössler [2,3], Loren [4,5], and the so-called double scroll circuit [6]. Experi mental work, often conceived with respect to possib communication applications, has mainly been done coupled Lorenz-based circuits [7], Rössler systems [8 Chua circuits [9], and lasers [10]. The impact of the choice of coupling scheme on th synchronizing outcome is a matter of current interest [11 A fundamental factor is whether bidirectional (mutual) o unidirectional coupling is assumed. Many examples the latter are to be found: Duffing’s equations [12], Loren model [13], Rössler systems [14], mixed Lorenz-Rössl [15], and unidirectionally coupled analog circuits [16,17] The behavior of a unidirectionally coupled pair o chaotic pendula is the subject of this Letter. Harmon cally driven pendula have often served as prototypic chaotic systems [18]. Beyond the rewards to be foun in exploring the rich dynamics of the pendulum within th context of contemporary nonlinear dynamics, this syste possesses the additional significance of being an ana of a capacitive Josephson junction—a superconducti device of considerable practical importance [19]. In this work we find that permanent synchronization o the two pendula does not occur except as a numerical a fact arising from finite computational precision. Instead intermittent locking is seen to be an essential property this system. These results constitute a warning that c must be exercised in assessing the results of numeri studies which apparently lead to synchronized chaos. The master pendulum is described in dimensionle form by the usual nonautonomous expression in the a gular coordinateum