Метод определения характеристик перемежающейся обобщенной синхронизации, основанный на вычислении вероятности наблюдения синхронного режима

Method to define the characteristic phases in the behavior of unidirectionally coupled systems being near the boundary of the generalized chaotic synchronization regime onset, based on calculation of the probability of the synchronous regime observation in ensemble of coupled systems is proposed. Using the example of unidirectionally coupled Rössler systems in the band chaos regime we show its efficiency in comparison with the other known methods for detection the characteristics of intermittent generalized synchronization.

Mutual synchronization of complex structures in interacting ensembles of non-locally coupled rotators

Background and Objectives: One of the actual problems in nonlinear dynamics is the formation and interaction of complex spatial structures such as chimeras and solitary states arising in multicomponent systems. Chimera states are typical for ensembles of identical oscillators with regular, chaotic, and even stochastic behavior in a case of nonlocal interaction of the elements. They represent cluster structures, including groups of elements with synchronous and non-synchronous oscillations. Chimeras were discovered and investigated in real experiments, that indicates the possibility of observing such regimes in complex systems in living nature and in technology. Solitary states are less studied today. The regime of solitary states is characterized by the synchronous behavior of most elements of the ensemble, while individual oscillators behave in a “special state”. In the present work, an ensemble of phase oscillators with inertia (rotators) is chosen as the basic model for investigation. Such ensembles with a specific coupling topology are widely used in modeling the operation of energy networks. Ensembles of rotators with nonlocal coupling are characterized by both chimera states and solitary state regimes. The problem of interaction of ensembles of rotators with nonlocal coupling and synchronization of complex spatial structures (chimeras and solitary states) formed in them has not been studied yet. Materials and Methods: A two-layer multiplex network of rotators with a nonlocal character of intralayer interactions is considered. Each layer consists of 100 elements with the same value of the coupling coefficient and coupling phase shift for each element within one layer. The interlayer coupling is symmetric. At the initial stage, with a random choice of initial conditions, steady regimes (chimeras or solitary states) in non-interacting layers were found. Next, the interlayer coupling was introduced and the evolution of the layer dynamics in the selected initial regimes was studied. Four cases of interaction with various initial states of the layers were considered. In the first case, the two layers are completely identical and demonstrate slightly different chimera structures without interlayer coupling. Their evolution with the introduction and growth of the interlayer coupling is considered for two values of the coupling phase shift. It is shown that, starting from a certain threshold value of the interlayer coupling coefficient, the complete synchronization regime is established in the layers, and the coupling phase shift significantly affects the value of the synchronization threshold. In the second case, the previous experiment is reproduced for the two layers with a frequency mismatch. Chimera states established without interlayer interaction are characterized by significantly different average frequencies of the elements in the two layers. In the presence of non-identity of the layers (in this case, frequency mismatch), the regime of complete synchronization of spatial structures is impossible. However, with an increase in the interlayer coupling coefficient, effective synchronization can be obtained which corresponds to a slight difference in the phases of rotators in the interacting layers with full frequency synchronization. In the third case, we consider the interaction between the layers in the solitary state regimes with different spatial structures. In this case, a frequency mismatch is also introduced for the elements of the two layers. For solitary states, the effective synchronization regime with an increase in the interlayer coupling is also established. In both layers the same configurations of solitary states are realized and frequency synchronization is observed. In the fourth case, a heterogeneous multiplex network is considered, in which one layer is in the chimera state, the second layer shows the solitary state mode. With a certain strength of the interlayer coupling the complex structures are destroyed in both layers of the network and a spatially uniform regimes are established. In this case, all the rotators of the two layers rotate at the same frequency, and the difference in the regimes in the layers reduces to a small phase shift, the same for all pairs of coupled rotators of the two layers. Conclusion: The effects of synchronization in the multiplex network were established for two layers in the regimes of complex spatio-temporal dynamics, such as chimera states and solitary states. The influence of the frequency mismatch of the network elements and the phase shift in the interlayer coupling on the synchronization phenomena was studied.

Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова

Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

Корректность определения характеристик перемежающейся обобщенной синхронизации при использовании только одной переменной ведомой и вспомогательной систем

Method for detection of characteristic phases of behavior in the intermittent generalized synchronization regime based on the use of an auxiliary system is considered. It is found that for the correct determination of the type of intermittency realized in the system, it is sufficient to use the only one variable characterizing the state of this system.

Особенности обобщенной синхронизации в системах с запаздыванием

Peculiarities of the generalized synchronization regime in unidirectionally coupled time-delayed generators are studied. Four different cases of interaction between systems characterized by different number of positive Lyapunov exponents are considered. The thresholds of the generalized synchronization regime onset is found to depend sufficiently on the degree of chaotic states of interacting systems, whereas the coupling between systems characterized by different number of positive Lyapunov exponents results in appearance of additional synchronous fields.

Anticipated Synchronization and Zero-Lag Phases in Population Neural Models

Anticipated synchronization is a counterintuitive synchronization regime between a master and a slave dynamical system in which there is a negative phase difference between the driver and the driven system. By studying a set of simple neural oscillators, we unveil the dynamical mechanisms required to generate this phenomenon. We study master–slave configurations where the slave system is, when uncoupled, in a quiescent excitable state. We exemplify our results by describing the dynamics of a dynamical system proposed to model the part of a songbird’s brain involved in song production.

Experimental Investigation on the Suppression Device of VIV of a Flexible Riser

Experimental investigations were conducted on a flexible riser with and without helical strakes. A uniform current was obtained by towing a riser model in a tank, and the vortex-induced vibration (VIV) suppression of strakes with different heights and pitches was studied. The results of the bare riser show that the characteristics of the synchronization of the VIV for a flexible riser have many orders, and the excited mode jumps from one to another abruptly. During the high order synchronization regime, the VIV response decreases with the increased order of the synchronization. The experimental results also indicate that the response characteristics of a bare riser can be quite distinct from those of a riser with helical strakes, and the suppression performance depends on the geometry of the helical strakes. The fatigue damage in the CF direction is of the same order as that in the IL direction for the bare riser. However, for the riser fitted with helical strakes, the fatigue damage in the CF direction is much smaller than that in the IL direction. The experimental results also confirmed that strake height has a greater influence on the VIV response than the strake pitch, and the drag exerted on the riser increases with strake pitch and height.