Synchronization Mode Transitions Induced by Chaos in Modified Morris-Lecar Neural Systems with Weak Coupling

Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak electrical and chemical coupling are respectively investigated. For the two coupled neurons, by increasing the calcium conductivity, it is found that the period-2 synchronization of action potential of neurons is transformed to desynchronization first, and then to period-3 synchronization. By increasing the potassium conductivity, however, the synchronization mode transition is a reversal direction process as mentioned above. The bifurcation analysis of inter-spike interval shows that the synchronization modes transition is induced by the chaos. The stronger the coupling strength is, the smaller the period-2 synchronization region in the parameters plane is, while the larger the period-3 synchronization region will be. For the star-coupled neural network, in the presence of weak electrical coupling, it can exhibit the complete synchronization, desynchronization, and drum head mode states under different parameter values, respectively. In the presence of chemical synapse, however, the completely synchronized state can not be observed in the star-coupled neural network. Our results might provide novel insights into synchronization modes transition and related biological experiments.

Analysis of Steady-State Oscillations in an Autonomous Oscillator under Multi-Frequency Excitation

The analysis of the behavior of an oscillator under multi-frequency excitation is considered in the paper. The investigation is based on the phase macromodel. The paper shows that three steady-state modes can exist in oscillator under multi-frequency excitation. The synchronized (locked) mode can be defined as the coincidence of the oscillator fundamentals with the excitation fundamentals in the region of sufficiently large excitation magnitude. The unsynchronized (unlocked) mode exists outside the synchronized region and its spectrum contains additional intrinsic fundamental besides the excitation ones. Singular points mode in some isolated points outside the synchronized region is characterized by the equality of the number of the oscillator fundamentals with the number of the excitation fundamentals. Performed numerical experiments confirmed the appearance of bifurcation points while transition of oscillator into the synchronization mode. The existence of singular points outside the synchronization region and their isolated character was also experimentally demonstrated. The problems of finding a steady-state solution of the phase equation of an excited oscillator by the Harmonic Balance (HB) method are considered. It is shown that main difficulties are connected with the presence of linear term in the steady-state solution. A transformation is proposed to provide the formation of HB equations for the phase micromodel in a standard form. Additional difficulties of HB simulations of synchronized oscillator phase equations are discussed.

Synchronization of Periodic Self-Oscillators Interacting via Memristor-Based Coupling

A model of two self-sustained oscillators interacting through memristive coupling is studied. The memristive coupling is realized by using a cubic memristor model. Numerical simulation is combined with theoretical analysis by means of quasi-harmonic reduction. It is shown that the specifics of the memristor nonlinearity results in the appearance of infinitely many equilibrium points which form a line of equilibria in the phase space of the system under study. It is established that the possibility to observe the effect of phase locking in the considered system depends on both parameter values and initial conditions. Consequently, the boundaries of the synchronization region are determined by the initial conditions. It is demonstrated that introducing or adding a small term into the memristor state equation gives rise to the disappearance of the line of equilibria and eliminates the dependence of synchronization on the initial conditions.

Comparative Study of Piezoelectric Vortex-Induced Vibration-Based Energy Harvesters with Multi-Stability Characteristics

This work reports a comparative study on piezoelectric energy harvesting from vortex-induced vibration (VIV) with multi-stability characteristics by introducing the nonlinear magnetic forces. A lumped-parameter model for the piezoelectric cantilever-cylinder structure is considered for the sake of qualitative investigation. Firstly, the buckling displacement of harvester in monostable and bistable configurations is evaluated by virtue of a static analysis. Then, the coupled frequency and damping of the harvester varying with the electrical load resistance are determined for different values of the spacing distance between magnets. Subsequently, the dynamic behaviors and generated voltage of the harvester in two configurations are elaborately investigated, showing that varying the spacing distance is followed by a shift of lock-in region which is significant for performance optimization according to ambient wind conditions. In addition, the results show the harvester in monostable configuration displays a hardening behavior while a softening behavior takes place in bistable configuration, both of the harvester in two configurations can widen the synchronization region.

Nonlinear vortex-induced vibration dynamics of a flexible pipe conveying two-phase flow

In this article, a vortex-induced vibration prediction model of a flexible riser conveying two-phase flow, including geometric and hydrodynamic nonlinearity, is established. A van der Pol wake oscillator is utilized to characterize the fluctuating lift forces. The finite element method is chosen to solve the coupled nonlinear fluid–structure interaction equations. The natural frequencies of the flexible riser are calculated to validate the method through comparisons with results from the literature. The modal analyses show that geometric nonlinearity has a significant effect on the natural frequency, and the critical internal velocity is reduced than those in linear analyses. The impacts of the gas volume fraction as functions of cross-flow velocity on the synchronization region, the displacement amplitudes, and the maximum stresses and frequency spectra have been investigated. The results show that an increase in the gas fraction results in the linear increase in natural frequencies and a wider synchronization region, and an increase in liquid flow rate led to the slight decrease in displacement amplitude and maximum stress within a small flow range.

Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System

Exploring the dynamics feature of robust chaotic system is an attractive yet recent topic of interest. In this paper, we introduce a three-dimensional fractional-order chaotic system. The important finding by analysis is that the position of signalx3descends at the speed of 1/cas the parameterbincreases, and the signal amplitude ofx1,x2can be controlled by the parametermin terms of the power function with the index −1/2. What is more, the dynamics remains constant with the variation of parametersbandm. Consequently, this system can provide rich encoding keys for chaotic communication. By considering the properties of amplitude and position modulation, the partial projective synchronization and partial phase synchronization are realized with linear control scheme. The distribution map of optimal synchronization region in the control-parameter space is charted by defining the power consumption of controller. Numerical simulations are executed to confirm the theoretical analysis.

Branch/mode competition in the flow-induced vibration of a square cylinder

The flow-induced vibration response of a square cross-sectional cylinder with low mass and damping ratio is analysed using continuous wavelet transforms (CWT) for three representative angles of attack of the cylinder to the incoming flow. The amplitude and frequency responses over a range of flow velocities map out multiple regimes (branches) of oscillation. Analysis of the time–frequency domain for boundary regions between branches using CWT reveals intermittency at the synchronization region boundaries as well as mode competition at branch boundaries. Complementary recurrence analysis shows that periodic dynamical states are interrupted by chaotic bursts in the transition regions around the higher branch at an angle of attack of α = 20° (a new branch first observed by Nemes et al. (2012 J. Fluid Mech. 710 , 102–130 ( doi:10.1017/jfm.2012.353 ))), supporting the CWT-based frequency–time analysis. This article is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.

Mitigation of Vortex-Induced Vibrations of a Pivoted Circular Cylinder Using an Adaptive Pendulum Tuned-Mass Damper

A novel adaptive pendulum tuned-mass damper (TMD) was integrated with a two degree-of-freedom (DOF) cylindrical structure in order to control vortex-induced vibrations of the structure. The natural frequency of the TMD was adjusted autonomously in order to control the vortex-induced vibrations. The experiments were performed at a constant Reynolds number of 2100 and for four reduced velocities, 4.18, 5.44, 6.00, and 6.48. Two TMD damping ratios, 0 and 0.24, were investigated for a constant TMD mass ratio of 0.087. The results demonstrate that tuning the natural frequency of the TMD to the natural frequency of the structure decreases the amplitudes of transverse and streamwise vibrations of the structure significantly. Specifically, the transverse amplitudes of vibrations are decreased by a factor of ten and streamwise amplitudes of vibrations are decreased by a factor of three. Depending on the value of the TMD damping ratio, the frequency of transverse vibrations is either characterized by the natural frequency of the structure or by two other fundamental frequencies, one higher and the other lower than the natural frequency of the structure. The results demonstrate that, independent of the TMD damping and tuning frequency ratios, the frequency of streamwise vibrations matches that of the transverse vibrations in the synchronization region, and the cylinder traces elliptic trajectories. A mathematical model is proposed to gain insight into the frequency response of the structure and fluid-structure interactions. The model shows that, for low TMD damping ratios, the frequency response of the structure equipped with the TMD is characterized by two fundamental frequencies; whereas, for relatively high TMD damping ratios, the frequency response of the structure is characterized by a single frequency, i.e., the natural frequency. In both cases, the fluid forcing within the synchronization region is linked to the fundamental frequency/frequencies of the structure. Thus, the classical definition of synchronization applies to multiple DOF structures undergoing vortex-induced vibrations.

Two-Degree-of-Freedom Flow-Induced Vibrations of a Circular Cylinder With a High Moment of Inertia Ratio

Two degree-of-freedom vortex-induced vibrations of a moderate mass and high moment of inertia ratio pivoted cylinder were investigated experimentally. The experiments were performed at a constant Reynolds number of 2100 for a range of reduced velocities from 3.4 to 11.25. The results show that, in addition to the reduced velocity, the transverse damping ratio has a significant effect on the amplitudes of response. The cylinder tip is observed to trace orbital trajectories, which is shown to be attributed to the frequencies of oscillations in both directions locking onto the natural frequency in the synchronization region. The results indicate that a phase angle between the streamwise and transverse oscillations governs the direction and orientation of the orbiting motion. Flow visualization results show that, at a given reduced velocity and transverse damping ratio, near-wake development changes along the cylinder span. The observed shedding patterns are shown to differ from those expected at the corresponding experimental parameters for one-degree-of-freedom uniform amplitude cylinder vibrations.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.