Manifestations of intermittency in unidirectionally coupled Pierce diodes on different time scales

Abstract

Intermittent behavior in unidirectionally coupled Pierce diodes being a classical model of spatially extended beam-plasma systems on different time scale is studied. Depending on the value of the strength of coupling between interacting systems and selected time scale, the ring intermittency, the eyelet intermittency or coexistence of both of them are shown to be observed.Keywords Intermittent behavior · Spatially extended systems · Unidirectionally coupled Pierce diodes · Phase synchronization · Time scale · Ring intermittency · Eyelet intermittency · Coexistence of ring and eyelet intermittencies Intermittency is one of the widespread phenomena in nonlinear science [1][2][3][4][5][6][7][8]. It is observed in flow systems, discrete maps and spatially distributed media. It is one of the classical scenarios of the transition to chaos and can also take place near the boundaries of different types of chaotic synchronization [9][10][11][12][13][14][15]. Intermittency manifests itself on the different time scales. In particular, in the phase synchronized flow chaotic systems the ring intermittency is observed on the boundary time scales [16], whereas near the boundary of the phase synchronization depending on the selected time scales the ring intermittency, the eyelet intermittency or coexistence of both types of intermittency mentioned above can take place [17]. Each type of the intermittency is characterized by its own statistical characteristics determined by the mechanisms (which are also different for the distinct intermittencies) resulting in the intermittent dynamics. These statistical characteristics (the distributions of the laminar and turbulent phase lengths calculated for the fixed values of the control parameters, the dependence of the mean length of the laminar phases on the control parameter and/or parameters of analysis) are used frequently to classify the type of intermittent behavior observed in the experimental or theoretical studies.Spatially extended nonlinear systems (including active media, complex networks and living objects) are also known to exhibit intermittent behavior [3,5,6,[18][19][20][21]. At the same time, the most part of known papers is devoted to the consideration of the coupledmap lattices, complex networks or dynamics of spatially distributed active media, whereas transitions from the asynchronous dynamics to different types of chaotic synchronization in such systems have not been studied in detail now. As an exception, one can refer to the papers [14,15] where intermittent phase and generalized synchronization has been studied, with the mechanisms of the synchronous regime arising and statistical characteristics of intermittency being the same as in the case of the systems with a small number of degrees of 123