Bistable Wave Research Articles

Analytical method for an excitation adaptive bistable wave energy converter

Analytical method for an excitation adaptive bistable wave energy converter

Wave Speeds for a Time-Periodic Bistable Three-Species Lattice Competition System

In this paper, we consider propagation direction (which can be used to predict which species will occupy the habitat or win the competition eventually) of a bistable wave for a three-species time-periodic lattice competition system with bistable nonlinearity, aiming to address an open problem. As a first step, by transforming the competition system to a cooperative one, we study the asymptotic behavior for the bistable wave profile and then prove the uniqueness of the bistable wave speed. Secondly, we utilize comparison principle and build up two couples of upper and lower solutions to judge the sign of the bistable wave speed which partially provides the answer to the open problem. As an application, we reduce the time-periodic system to a space–time homogeneous system, we obtain the corresponding criteria and carry out numerical simulations to illustrate the availability of our results. Moreover, an interesting phenomenon we have found is that the two weak competitors can wipe out the strong competitor under some circumstances.

The sign of bistable wave speed for a plankton model

The sign of the speed of bistable traveling wave solution is an important focus in the field of population dynamics, since it can be used to predict which species will win the competition and ultimately survive. In this paper, the sign of bistable wave speed of a plankton model with cubic nonlinearity is studied. By a delicate analysis, a sufficient condition for bistable wave to be stationary is first obtained. Symmetric and multiplication properties for stationary bistable wave are established. By upper-lower solution method and comparison principle, two sufficient conditions are found so that the bistable wave speed is negative or positive. Moreover, numerical simulations are performed to illustrate our theoretic conclusions.

Bistable spiral wave dynamics in electrically excitable media.

We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.

A bistable point absorber wave energy convertor with a mechanical motion rectifier

The design of novel wave energy converters (WECs) with the capability of low frequency energy capture is of great significance for the development of low frequency ocean wave energy. In this study, a novel point absorber WEC combined with a bistable mechanism and a mechanical motion rectifier (MMR) is proposed to achieve the goal of efficiently capturing wave energy in the low frequency range. In the WEC, the introduction of a rack-pinion-lever-spring (RPLS) bistable mechanism can not only enhance the capture efficiency in a low frequency range but also protect the system from excessive vibration amplitude through the nonlinear stiffness. Besides, one MMR based power take off (PTO) system is proposed to convert the bidirectional vibration into unidirectional rotation of the generator and extract more power via the mechanism of two one-way pinions. The dynamic model in the time domain for the nonlinear point absorber WEC with the RPLS bistable mechanism and the MMR based PTO system is established in which the convolution term is replaced by the state space method. The characteristics of the nonlinear dynamics and wave energy capture performance for the novel WEC are analysed in regular wave condition. The numerical results demonstrate that the peak capture width ratio of the proposed WEC can reach almost 2 times that of the traditional linear system in a lower frequency range.

High efficiency and wideband wave energy capture of a bistable wave energy converter with a displacement amplifier

Ocean wave energy is a kind of renewable energy with huge reserves, which can play an important role in the future construction of smart oceans. The low capture efficiency and narrow bandwidth of traditional wave energy capture devices seriously restrict the large-scale application of wave energy. To address these issues, a rack-pinion-lever-spring (RPLS) adaptive bistable Power Take-Off (PTO) mechanism with a time-varying potential barrier is proposed and applied to a point absorber wave energy converter (WEC). In the proposed nonlinear PTO system, a rack-pinion-lever (RPL) mechanism, as a displacement amplifier, has an effect on enhancing the poor amplitude sensitivity issue of the negative stiffness mechanism. Based on linear wave theory, a special nonlinear one-and-half-degree of freedom dynamic model is developed to describe the adaptive bistable wave energy converter (AB WEC). In comparison with the traditional bistable WEC (TB WEC) and equivalent linear WEC, the numerical results show that the AB WEC can greatly enhance the capture efficiency of lower frequency energy, especially at small wave excitations. The energy capture efficiency of the AB WEC is close to that of the TB WEC even at large wave amplitudes and is higher than that of the equivalent linear WEC. Finally, the wave energy capture characteristics of the three kinds of systems are studied based on the wave distribution diagram of a certain sea area in the South China Sea. The results show that the AB WEC has a large wave height adaptability in the low frequency region. The AB PTO mechanism with a displacement amplifier proposed in this paper can provide a technical reserve for the highly efficient and wide bandwidth capture of low frequency ocean wave energy.

Experimental assessment of the performance of a bi-stable point wave energy absorber under harmonic incident waves

Intentional introduction of a bi-stable nonlinear restoring element to the design of point wave energy absorbers (PWAs) has been recently investigated as a means to broaden the steady-state response bandwidth of the PWA and shift it towards lower frequencies. The underlying hypothesis, which is supported by many previous theoretical investigations, is that this will help (i) reduce the sensitivity of the PWA’s response to variations in the frequency and amplitude of the incident waves, and (ii) permit the PWA to effectively harness energy from the low-frequency high-energy content of the incident wave spectrum. In this study, we investigate this hypothesis experimentally by designing, fabricating, and assessing the response behavior of a prototype bi-stable PWA (B-PWA) excited by harmonic incident waves in an experimental wave flume. We create bifurcation maps in the wave frequency and amplitude parameters’ space and use them to define an effective frequency bandwidth outside which the B-PWA generates negligible power levels. We compare the effective bandwidth of three different B-PWAs (different bi-stable restoring elements) to the traditional linear design and demonstrate that bi-stability does not seem to improve the effective bandwidth over the linear design; at least not for the three designs considered. Moreover, the difficulty of defining the effective bandwidth of the B-PWA and its sensitive dependence on the wave amplitude adds more layers of complexity, which make the process of optimizing its performance a cumbersome task. Nonetheless, a key advantage remains in the ability of the bi-stable restoring force to push the effective bandwidth of the B-PWA towards lower frequencies, where most of the wave energy is trapped.

Impact of nonlocal dispersal and time periodicity on the global exponential stability of bistable traveling waves

AbstractGlobal exponential stability of bistable traveling wave solutions to a periodic Lotka–Volterra system with nonlocal dispersal is investigated. We first establish refined squeezing upper and lower solutions based on the properties of the bistable wavefront. This important squeezing technique has been successfully applied to study the exponential convergence of solutions.

Bistable pulsating wave of a competition model in rapidly varying media and its homogenization limit

This paper is concerned with the existence of bistable pulsating wave for a two-species competition system in rapidly periodically varying media and its homogenization limit as the spatial period tends to zero. Assuming that the homogenized system admits a bistable traveling wave, we first show the existence of pulsating wave for all small periods and determine the homogenization limit of the wave speed. Furthermore, in the case where the homogeneous wave is not stationary, we investigate the effects of spatial heterogeneity on the wave speeds. Our estimates indicate that the deviation of the wave speeds in comparison to the homogeneous one is at most linearly along with small period in the general case, and is of second order where the heterogeneity appears only in the diffusion coefficients.

Bistable traveling waves in a delayed competitive system

<p style='text-indent:20px;'>This paper is concerned with the existence, uniqueness and asymptotic stability of traveling wave solutions in a delayed competitive system with spatial diffusion. When the interspecific competition is strong, the corresponding functional differential system has two stable and two unstable steady states. Firstly, we establish the existence of bistable traveling wave solutions by the theory of monotone semiflows. With the help of squeezing technique based on comparison principle, the asymptotic stability of traveling wave solutions is proved, which further implies the uniqueness of wave speed and wave profile in the sense of phase shift.</p>

Spreading speed of a lattice time-periodic Lotka–Volterra competition system with bistable nonlinearity

We study the uniqueness and sign of bistable wave speed for a lattice time-periodic Lotka–Volterra competition system of bistable type. The sign of wave speed reflects the propagation direction of traveling wave which arises as a challenging problem in the field of traveling wave theory. Actually, even for the case of homogeneous environment, there is no common method that can be used to deal with it. First, we show that the speed of the bistable wave of the model is unique. Second, by making use of upper–lower solution method and comparison principle, a set of explicit conditions is built up such that the sign of the wave speed can be justified. From the viewpoint of biology, these conditions reveal which of the species will tend to extinction and which will survive when the environment changes periodically in time.

The bistable wave speed in a reaction-diffusion system with seasonal succession

In this paper, we are concerned with the speed of time-periodic bistable traveling waves in a reaction-diffusion competition system with seasonal succession. The value range of the speed is obtained by applying a comparison principle and the uniqueness and stability of time-periodic bistable traveling waves. The comparison principles on speeds between the time-periodic bistable wave and upper or lower solutions are established. Then by constituting explicitly upper or lower solutions we then derive some certain conditions on parameters under which the positive or negative speeds are realized. More significantly, we find concrete examples for the considered reaction-diffusion system with half the good seasons and half the bad seasons, so that the theoretical results are corroborated by numerical simulations.

Bistable traveling waves for time periodic reaction-diffusion equations in strip with Dirichlet boundary condition

We study the existence of bistable traveling wave solutions for time periodic reaction-diffusion equations in straight strips subject to the Dirichlet boundary condition. We first employ a monotone dynamical system framework to establish the existence of such a wave by assuming a bistability structure in terms of multiplicity and stability of periodic solutions in the section of the strip, which is then realized under a set of sufficient explicit conditions; in particular, the bistability structure appears if the reaction term is a time periodic smooth perturbation of the nonlinearity λu(1−u)(u−a) when a∈(0,1/2) and λ>λ⁎ for some λ⁎>0.

Response behavior of bi-stable point wave energy absorbers under harmonic wave excitations

To expand the narrow response bandwidth of linear point wave energy absorbers (PWAs), a few research studies have recently proposed incorporating a bi-stable restoring force in the design of the absorber. Such studies have relied on numerical simulations to demonstrate the improved bandwidth of the bi-stable absorbers. In this work, we aim to understand how the shape of the bi-stable restoring force influences the effective bandwidth of the absorber. To this end, we use perturbation methods to obtain an approximate analytical solution of the nonlinear differential equations governing the complex motion of the absorber under harmonic wave excitations. The approximate solution is validated against a numerical solution obtained via direct integration of the equations of motion. Using a local stability analysis of the equations governing the slow modulation of the amplitude and phase of the response, the loci of the different bifurcation points are determined as function of the wave frequency and amplitude. Those bifurcation points are then used to define an effective bandwidth of the absorber. The influence of the shape of the restoring force on the effective bandwidth is also characterized by generating design maps that can be used to predict the kind of response behavior (small amplitude periodic, large amplitude periodic, or aperiodic) for any given combination of wave amplitude and frequency. Such maps are critical toward designing efficient bi-stable PWAs for known wave conditions.

Bistable wave-speed for monotone semiflows with applications

The sign of bistable wave speed indicates the propagation direction of bistable wavefronts. This paper deals with the propagation dynamics of bistable traveling waves for abstract monotone semiflows. We first prove that the bistable wave speed is unique and bounded by spreading speeds of two mono-stable subsystems. We then establish speed-sign determinacy by way of comparison principles. Based on these results, for both irreducible and reducible cases we derive general conditions for determining the speed sign. Finally, the obtained theory is applied to three kinds of evolution systems.

Parametric study on power capture performance of an adaptive bistable point absorber wave energy converter in irregular waves

The power capture performance of an adaptive bistable point absorber wave energy converter (WEC) in irregular waves is investigated in this paper. Based on the linear potential flow theory and Cummins equations, the equation of motion for the WEC is established in time domain. Then a parametric study is performed on the power capture performance of the WEC by considering the influences of different wave and system parameters such as the spring combination parameter, the stiffness of auxiliary springs and main springs, the original length value of the main spring, damping coefficient of the PTO systems and the significant wave height. The results show that in an irregular wave, each parameter will have a certain impact on the performance of the device. Appropriate device parameters need to be selected according to actual environmental parameters to ensure that the adaptive bistable WEC has better power capture performance than its linear and conventional bistable counterparts.

Evaluation of long-term power capture performance of a bistable point absorber wave energy converter in South China Sea

Nowadays, extensive research has been conducted to generate electricity from ocean waves, but there are not too many studies on the capture of wave energy in a specific ocean area. As the largest sea area in China's offshore waters, the South China Sea contains a large amount of wave energy and is regarded as a natural wave energy power plant. A comparative study was conducted to investigate the effects of wave energy converter (WEC) parameters on the long-term power capture performance of a bistable point absorber WEC installed in the South China Sea in this paper. Combined with the joint probability distribution of significant wave height Hs and peak wave period Tp in South China Sea, a mathematical model was developed for the evaluation of long-term power performance of WECs. The governing equations of the point absorber WEC were established using the hybrid frequency-time domain method. The dynamic response and captured power can be obtained after numerically solving the equations of motion with the 4th order Runge-Kutta Method. The results show that the bistable mechanism has great advantages in the long-term captured power of WEC. In general, a circular truncated cone-shaped buoy WEC with a larger buoy size and smaller nonlinear parameter tend to result in better long-term power capture performance. The insights given in this study provide a motivation and foundation for developing a complete set of performance optimization methods of point absorber WECs installed in South China Sea.

A bistable X-structured electromagnetic wave energy converter with a novel mechanical-motion-rectifier: Design, analysis, and experimental tests

Beneficial nonlinearities have been intentionally introduced to improve energy harvesting performance. However, few results are reported on the issues of exploiting bistable and quasi-zero stiffness structures or mechanisms simultaneously to enhance ocean energy conversion in the literature. In this study, a novel bistable electromagnetic wave energy converter is proposed, which includes a bio-inspired X-shaped supporting structure/mechanism and a mechanical-motion-rectifier. This is for the first time that the bistable stiffness and quasi-zero stiffness are employed together (in all working range) to strengthen wave energy conversion, by developing a novel bistable X-structured system as a wave energy converter, which can bear with large vibration stroke simultaneously. Additionally, a novel mechanical-motion-rectifier with a novel energy-storing-releasing mechanism is specially designed as the power take-off system to convert linear motion to rotary motion, which greatly improves the instant voltage and power generated. The novel X-structured system demonstrates very designable nonlinear bistable and quasi-zero stiffness and thus can significantly enhance the wave energy conversion performance. Compared with traditional linear converters, much more power can be generated, especially in the low-frequency range due to the quasi-zero and bistable properties. The experiments show that, with the wave height of 0.15 m as well as the wave period of 4 s, it can generate a voltage peak at around 15 V and a power peak at about 1 W. The present results indicate that, the proposed nonlinear bistable X-structured system holds promising potentials in acting as a floating-point energy converter, which could power seashore environmental monitoring systems and wireless communication devices for smart oceans.

Improved bistable mechanism for wave energy harvesting

As one of the renewable and clean energy sources, wave energy has high density and all-day availability characteristics. However, the development of wave energy converters has been hampered, mainly because of the low efficiency induced high levelized energy costs. The present study introduces an improved bistable mechanism composed of three linear springs, aiming to enhance the performance of a point absorber employed as a wave energy converter. The improved bistable mechanism features an asymmetric configuration of three linear stiffness springs: one horizontal and two obliques on a vertical plane. Numerical simulations based on Cummins equations in the time domain describe the point absorber dynamic behavior in regular and irregular waves. The improved bistable wave energy converter featured a wider low equivalent stiffness range than linear and conventional bistable counterparts, improving its ability to frequency shifting. Its lower potential barrier greatly improves the capture width ratio and frequency bandwidth at low excitations. Such characteristics facilitate the improved bistable wave energy converter to achieve higher efficiency than its linear and conventional bistable counterparts at low frequencies, and enhance its robustness against power-take-off damping detuning and sea state changes. These features altogether make the improved bistable mechanism an efficient alternative to explore the benefits of the bistable dynamics applied to wave energy converters.

High-performance and robust bistable point absorber wave energy converter

A novel magnetic bistable device (MBD) is proposed to improve the efficiency of energy harvesting of a point absorber wave energy converter (WEC) by decreasing the potential barrier of the bistable energy absorber. The novel MBD is mainly composed of two pairs of coaxial permanent magnet rings with different sizes. For the permanent magnet rings, one pair has the same magnetic field direction to provide negative stiffness and the other magnet rings have nonlinear positive stiffness property with a reverse magnetic field direction. The nonlinear dynamic model is established by adopting the state space model approach during solving the convolution integral of radiation force. The capture width ratio of the WEC with the novel MBD is studied with the change of design parameters in regular wave. Then the effect of structural parameters for the novel MBD on the wave energy capture ratio is discussed. The results indicate that using the novel MBD can significantly improve the performance of point absorber WEC especially under low wave excitations in comparison with that of the WEC with traditional MBD.