Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.

A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will help advanced graduate students and researchers gain an organic and complete understanding of the subject.

Multistability refers to the coexistence of different stable states in nonlinear dynamical systems. This phenomenon has been observed in laboratory experiments and in nature. In this introduction, we briefly introduce the classes of dynamical systems in which this phenomenon has been found and discuss the extension to new system classes. Furthermore, we introduce the concept of critical transitions and discuss approaches to distinguish them according to their characteristics. Finally, we present some specific applications in physics, neuroscience, biology, ecology, and climate science.

The understanding of neurophysiological mechanisms responsible for motor imagery (MI) is essential for the development of brain-computer interfaces (BCI) and bioprosthetics. Our magnetoencephalographic (MEG) experiments with voluntary participants confirm the existence of two types of motor imagery, kinesthetic imagery (KI) and visual imagery (VI), distinguished by activation and inhibition of different brain areas in motor-related α- and β-frequency regions. Although the brain activity corresponding to MI is usually observed in specially trained subjects or athletes, we show that it is also possible to identify particular features of MI in untrained subjects. Similar to real movement, KI implies muscular sensation when performing an imaginary moving action that leads to event-related desynchronization (ERD) of motor-associated brain rhythms. By contrast, VI refers to visualization of the corresponding action that results in event-related synchronization (ERS) of α- and β-wave activity. A notable difference between KI and VI groups occurs in the frontal brain area. In particular, the analysis of evoked responses shows that in all KI subjects the activity in the frontal cortex is suppressed during MI, while in the VI subjects the frontal cortex is always active. The accuracy in classification of left-arm and right-arm MI using artificial intelligence is similar for KI and VI. Since untrained subjects usually demonstrate the VI imagery mode, the possibility to increase the accuracy for VI is in demand for BCIs. The application of artificial neural networks allows us to classify MI in raising right and left arms with average accuracy of 70% for both KI and VI using appropriate filtration of input signals. The same average accuracy is achieved by optimizing MEG channels and reducing their number to only 13.