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.

Necessary Conditions for Complete Synchronization of a Coupled Chaotic Aihara Neuron Network with Electrical Synapses

In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

Star-coupled Hindmarsh–Rose neural network with chemical synapses

We analyze the patterns like synchrony, desynchrony, and Drum head mode in a network of Hindmarsh–Rose (HR) neurons interacting via chemical synapse in unidirectional and bidirectional star topology. A two-coupled system has been studied for synchronization by varying the coupling strength and the parameter describing the activation and inactivation of the fast ion channel. The transverse Lyapunov exponent spectrum is plotted to observe the point of transition from desynchrony to synchrony. The synchronized, desynchronized, and drum head mode regions are observed when the neurons are connected in unidirectional and bidirectional coupling configurations. A detailed analysis about the time evolution of membrane potential corresponding to each region is presented. The annihilation of synchronized region and the expansion of drum head mode region in bidirectional coupling is discussed using parameter space. Our work provides finer insight into the existence and stability of Drum head mode and is useful for designing communication networks.

Estimation of the Damping Parameter Governing the VIV of Long Flexible Cylinders

Much effort in the past half century has been made to explain the role of damping in the prediction of VIV. Scruton (1965), Griffin et al. (1975), Klamo, et al. (2005) and Govardhan & Williamson (2006) all made significant contributions. None fully characterized the role of damping in governing the response over the full range reduced velocities, which encompass the wake synchronized region. In 2012 Vandiver devised a way to do that with a new damping parameter c*. His results were verified using 2D spring-mounted cylinders in uniform flow. The primary objective of the research described in this paper is to find a c* -like quantity for flexible cylinders, which is capable of organizing response data for flexible cylinders, which may have many modes, be exposed to sheared flows and possess spatially varying properties, such as the coverage of strakes and fairings. Data from a recent high mode VIV model test campaign conducted by SHELL Exploration and Production Company are used to illustrate the application of c* to flexible cylinders. It is shown that, if one accounts for Reynolds number, the response of flexible cylinders with varying strake coverage in the SHELL Tests collapse onto a single curve.

Bifurcation Analysis of Synchronized Regions in Complex Dynamical Networks with Coupling Delay

According to the master stability function (MSF) framework, synchronized regions play an extremely important role in network synchronization. On these grounds, this paper casts sight on network synchronous state stability via studying the bifurcation (or transition) problem of network synchronized regions with varying nodal dynamics, and the effects of time delay on the bifurcation of synchronized regions. Theoretical and numerical investigations show that in complex networks with coupling delay, there exist rich bifurcation behaviors of synchronized regions. The coupling delay can not only enlarge or narrow synchronized regions, but also change bifurcation points. More importantly, a very small delay can result in the conversion of an unbounded or empty synchronized region into a bounded one, implying that coupling delay can enhance or suppress synchronization in complex dynamical networks. These results will further strengthen our understanding for synchronous state stability in complex dynamical networks.

EFFECT OF OUTDOOR PRESSURE FLUCTUATIONS ON NATURAL VENTILATION IN A ROOM WITH TWO OPENINGS

We investigated the effects of outdoor pressure fluctuations on natural ventilation in a room with two openings. One opening is exposed to an oscillating outdoor pressure and the other is exposed to a fixed neutral pressure. The ventilation airflow rate depends on the amplitude and period of the outdoor pressure fluctuations, the room volume, and the sizes of the openings. Dimensionless parameters are derived from the governing equations that determine indoor pressure responses due to outdoor pressure fluctuations. The pressure responses and the airflow rates through the openings are obtained using a fourth-order Runge–Kutta method. The flow regions are categorized into a synchronized region, an opening resistance region, and a transition region, depending on the dimensionless parameters. Applications are considered using an example building space to investigate the effective air change rates depending on the size of the openings and the period of wind pressure fluctuations.

Complex Network Synchronizability: The Effect of Coupling Strength

In this paper, the effect of the coupling strength to the complex network synchronizability is investigated. For a given network with identical node dynamics, it is shown that the coupling strength among the nodes is one of key factors influencing the network synchronizability besides the network inner linking matrix and the eigenvalues of the network topological matrix. It is point that if the synchronized region is an unbounded sector, for achieving synchronizability, the coupling strength must be greater than or equal to the minimum coupling strength, and with the increasing of the coupling strength, network synchronizability is improved; if is a bounded sector, for achieving network synchronizability, the coupling strength must be in a certain range, and the larger coupling strength does not necessarily indicate better synchronizability.

Transition to Measure Synchronization in Coupled Hamiltonian Systems

The transition to measure synchronization in two coupled φ4 equations are investigated numerically both for quasiperiodic and chaotic cases. Quantities like the bare energy and phase difference are employed to study the underlying behaviors during this process. For transition between quasiperiodic states, the distribution of phase difference tends to concentrate at large angles before measure synchronization, and is confined to within a certain range after measure synchronization. For transition between quasiperiodicity and chaos, phase locking is not achieved and a random-walk-like behavior of the phase difference is found in the measure synchronized region. The scaling relationship of the phase distribution and the behavior of the bare energy are also discussed.

Velocity Correlation and Vortex Spacing in the Wake of a Vibrating Cable

The von Karman vortex streets formed in the wakes of vibrating, flexible cables were studied using hot wire anemometers. The experiments took place in or at the boundaries of the flow regime where the vibration and vortex-shedding frequencies lock together, or synchronize, to control the wake formation. Spacial cross-correlations of the wake velocity signals were made for Reynolds numbers between 400 and 1300. Within the synchronized region, the magnitude of the measured spanwise cross-correlation coefficient is seen to approach unity, being limited by turbulence but apparently independent of frequency, amplitude, and Reynolds number. The bounds of the lock-in regime are determined and compare remarkably well with previous vibrating, rigid cylinder results. Further, the downstream longitudinal vortex spacing and induced street velocity are also found to compare well with vibrating cylinder results.