Search

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

In this paper we propose an enhanced continuum model for traffic flow considering the effect of driver characteristics and traffic jerk. Based on the linear stability condition, the sufficient conditions of model stability is given. In the nonlinear stability analysis, we derive the KdV–Burger equation to describe the propagation characteristics of traffic density waves near the neutral stability curve. The simulation example verified that the driver characteristics and traffic jerk have a significant impact on the stability of the traffic flow and emissions.

Basic lattice model is extended to study the heterogeneous traffic by considering the optimal current difference effect on a unidirectional single lane highway. Heterogeneous traffic consisting of low- and high-sensitivity vehicles is modeled and their impact on stability of mixed traffic flow has been examined through linear stability analysis. The stability of flow is investigated in five distinct regions of the neutral stability diagram corresponding to the amount of higher sensitivity vehicles present on road. In order to investigate the propagating behavior of density waves non linear analysis is performed and near the critical point, the kink antikink soliton is obtained by driving mKdV equation. The effect of fraction parameter corresponding to high sensitivity vehicles is investigated and the results indicates that the stability rise up due to the fraction parameter. The theoretical findings are verified via direct numerical simulation.

Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.

A new traffic lattice hydrodynamic model with consideration of on-ramp and off-ramp is proposed in this paper. The influence of on-ramp and off-ramp on the stability of the main road is uncovered by theoretical analysis and computer simulation. Through linear stability theory, the neutral stability condition of the new model is obtained and the results show that the unstable region in the phase diagram is enlarged by considering the on-ramp effect but shrunk with consideration of the off-ramp effect. The mKdV equation near the critical point is derived via nonlinear reductive perturbation method and the occurrence of traffic jamming transition can be described by the kink–antikink soliton solution of the mKdV equation. From the simulation results of space-time evolution of traffic density waves, it is shown that the on-ramp can worsen the traffic stability of the main road but off-ramp is positive in stabilizing the traffic flow of the main road.

Direct numerical simulations (DNS) were used to investigate the effect of frequency bandwidth on the laminar-turbulent transition of wavepackets evolving in a Blasius boundary layer under a total of 18 different combinations of wavepacket frequency, amplitude and bandwidth. Extensive comparisons with linear stability theory (LST) were also performed with a program written to automat- ically calculate the spatial amplification of an ensemble of modes in a wavepacket, enabling the linear and nonlinear aspects of the wavepacket development to be clearly distinguished. Input disturbances that are wide in terms of frequency bandwidth encouraged N-type (Novosibirsk) transition, while narrow-bandwidth disturbances favoured K-type (Klebanoff) transition. However, the initial amplitude and frequency composition of the wavepacket also play an important role in the transition process, with higher-amplitude initial disturbances leading to an increased number of K-type transition events, while frequency compositions that are dominated by linearly damped or slow-growing modes are more likely to transition via the N-route. Moreover, there is a certain preferred frequency of the wavepacket, corresponding to the lower branch point on the neutral stability curve at the disturbance source. The transition process appeared to be most sensitive to changes in bandwidth when the wavepacket is dominated by its preferred frequency.

A leading solution concept in the evolutionary study of extensive-form games is Selten's (1983) (selten1983evolutionary) notion of limit ESS. We demonstrate that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that “mutants” are arbitrarily rare relative to “trembling” incumbents. Finally, we present a novel definition that solves this issue and has appealing properties.

For the assessment of the safety of the Dutch flood defences extreme open-water winds need to be computed. There are, however, no sufficiently long and reliable in-situ data available. On the other hand, there is a rich dataset of decades of measurements at certain coastal and relatively close by inland stations. A commonly used two-layer model for neutral atmospheres was thought to provide reasonably accurate open-water winds from the available data, given that the model assumptions seemed plausible for the extreme winds of interest. However, the model results were deemed inaccurate and not usable. Given that this was unexpected, many of the model assumptions were analysed and, with the gained further insight, their validity and contribution to the invalidity of the deemed simple model approach assessed. Our conclusion is that the quality of the model results is significantly affected by at least two aspects: the assumption of neutral stability in the model, and – equally important – the assumption of independence between the surface roughness and the wind speed.

The original lattice hydrodynamic model of traffic flow is extended to single-file pedestrian movement at middle and high density by considering asymmetric interaction (i.e., attractive force and repulsive force). A new optimal velocity function is introduced to depict the complex behaviors of pedestrian movement. The stability condition of this model is obtained by using the linear stability theory. It is shown that the modified optimal velocity function has a remarkable influence on the neutral stability curve and the pedestrian phase transitions. The modified Korteweg–de Vries (mKdV) equation near the critical point is derived by applying the reductive perturbation method, and its kink–antikink soliton solution can better describe the stop-and-go phenomenon of pedestrian flow. From the density profiles, it can be found that the asymmetric interaction is more efficient than the symmetric interaction in suppressing the pedestrian jam. The numerical results are consistent with the theoretical analysis.

The vast majority of car-following models are lack of the consideration of human drivers’ characteristics. Based on the fact that each driver of a following vehicle perceives closing-in or shying-away a leading vehicle in front of him/her, primarily due to changes in the apparent size of the leading vehicle, we improved the full velocity difference (FVD) model and presented a visual angle car-following model. This model is in view of the stimulus–response framework and uses the visual angle and the change rate of the visual angle as stimulus. Results from linear analysis showed that the neutral stability line is asymmetry and the width of the leading vehicle has a great impact on the stability of traffic flow. Numerical simulations obtained the same results as theoretical analysis clearly such as density wave, shrinking hysteresis, asymmetry and wide scattering. Thus, the introducing of the visual angle can explain some complex nature of traffic flow and contribute to the design of more realistic car-following models.

In this paper, a new car-following model is proposed by incorporating the backward looking effect under certain conditions and multiple information of preceding cars in traffic flow. And the neutral stability condition of this model can be obtained by using the linear stability theory. Numerical simulation shows that the proposed model is theoretically an improvement over previous ones.

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.

The novel lattice hydrodynamic model is presented by incorporating the “backward looking” effect. The stability condition for the the model is obtained using the linear stability theory. The result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model. The Korteweg–de Vries (KdV, for short) equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by KdV soliton solution obtained from the KdV equation. The simulation result is consistent with the nonlinear analysis.

The spectral stability of compression solitons in non-linear elastic rods with respect to perturbations of the flexural mode of the oscillations of the rod is investigated. The system of equations of the isotropic theory of elasticity, taking account of the non-linear corrections corresponding to the interaction being studied, is used to describe the interaction of longitudinal and flexural waves in the rod. This system of equations describes long longitudinal-flexural waves of small but finite amplitude. It is shown that trapped flexural modes exist, which propagate together with a compression soliton. It is established that these modes, which are the least stable, do not increase with time.

The paper investigates the class of signaling games with the following properties: (a) the interests of sender and receiver coincide, (b) different signals incur differential costs, and (c) different events (meanings/types) have different probabilities. Necessary and sufficient conditions are presented for a profile to be evolutionarily stable and neutrally stable, and for a set of profiles to be an evolutionarily stable set. The main finding is that a profile belongs to some evolutionarily stable set if and only if a maximal number of events can be reliably communicated. Furthermore, it is shown that under the replicator dynamics, a set of states with a positive measure is attracted to "sub-optimal" equilibria that do not belong to any asymptotically stable set.

This paper gives a complete characterization of neutrally stable strategies for sender–receiver games in the style of Lewis, or Nowak and Krakauer [Lewis, D., 1969. Convention: A Philosophical Study. Harvard Univ. Press, Cambridge, MA; Nowak, M., Krakauer, D., 1999. The evolution of language. Proc. Nat. Acad. Sci. USA 96, 8028–8033]. Due to the dynamic implications of neutral stability, the replicator dynamics of this model does not necessarily lead to the rise of an optimal signaling system, where every state of the world is bijectively linked to one signal and vice versa, but it can be trapped in suboptimum situations where two (or more) signals are used for the same event, or two (or more) events are associated with one and the same signal.

Film flows down a vertical plane, the so-called falling films, are covered by waves whose lengths are longer than a threshold value corresponding to neutral stability of the waveless flow. On the other hand, experiments also demonstrate existence of the upper threshold wavelength in unstable interval. This phenomenon is explained through careful analysis of dynamical system modelling the wave dynamics in falling films.

The relative performance of two atmospheric dispersion models, the general finite line source model (GFLSM) and CALINE4, is assessed using carbon monoxide levels measured adjacent to a four lane motorway. The CALINE4 model has already been validated for Irish motorway conditions and the performance of the GFLSM is looked at under similar conditions. The performance of the model is tested using composite and hourly emission factors calculated with the COPERT III methodology. The model performed best for neutral stability conditions and wind speeds greater than 0.5 m/s. The modelled and predicted data were fitted to statistical distributions and it was found that the modelled and predicted data follow the Weibull distribution.

Some theoretical calculations of linear non-adiabatic pulsations of intermediate- and low- luminosity red giants in globular clusters have been carried out using a time-dependent theory of nonlocal stellar convection. As shown by the results, for all models with temperatures higher than 5400 K the modes up to the fourth overtone are pulsationally stable. With the increase of stellar luminosity, the low-order overtones also become pulsationally unstable. For red giants of intermediate and low luminosities, the pulsational stability is exceedingly low and is close to neutral stability. Therefore, they will be either non-variables or short-period variables (P

The morphological instability analysis is carried out for non-stationary solidification of a binary melt. We demonstrate that both the morphological and dynamic neutral stability curves coincide. The neutral stability curve for morphological perturbations does not intersect the self-similar branch of solutions for solidification, that is, the morphological instability does not cause the mushy zone origination whereas the constitutional supercooling arising ahead of the stable planar front solidifying in self-similar manner is a reasonable criterion for the mushy region incipience. The theory under consideration is in a good agreement with experimental and numerical studies carried out by Huppert and Worster.

The stability problem related to the basic flows induced by the peristaltic waves propagating along the deformable walls is investigated numerically. The neutral stability boundary is obtained by solving the relevant Orr–Sommerfeld equation via a verified preconditioned complex-matrix solver. The critical Reynolds number becomes 577.25 when the ratio of the wave speed to the maximum speed of the basic flow ( c / u max ) becomes 10.

A simple and useful formula for the critical wavelength in electrodeposition derived by Sundstrom and Bark is obtained under conditions less restrictive than those used in its original derivation.

The effect of accelerating stepwise on the jamming transition is investigated in the extended car-following model. The optimal velocity function is modified to take into account accelerating stepwise vehicles. It is shown that the multiple phase transitions occur on varying the car density. The multiple transitions change with the delay time. The flow-density curves and the velocity-headway curves are presented for various delay times. It is also shown that the multiple jamming transition lines are consistent with the neutral stability curves. The jamming transitions are closely related with the turning points of the optimal velocity function.

Gifford's (1959. Advances in Geophysics 6, 117–138) meandering plume model is extended to account for internal plume structure. The applicability of the model is thereby extended to include the near field of large sources and the far field. Agreement with measured root-mean-square fluctuating concentrations of scalars dispersing from elevated compact-area and line sources into surface layers with neutral stability is shown to be as good or better than that obtained with Gifford's model.

The neutral stability equation F(k, R)=0 for the Planar Benard Problem with non-slip boundary conditions is studied. It is proven that there is a pair (k ∗ , R ∗ ) in the domain of F for which F(k ∗ , R ∗ )=0 , such that if (k, R)≠(k ∗ , R ∗ ) is also in the domain and satisfies F(k, R)=0 then R>R ∗ . Approximations to k ∗ and R ∗ of guaranteed accuracy are given.

Wind tunnel experiments were carried out to study the effects of wind directional fluctuations on gas diffusion, under a neutral stability condition, over terrain models using the overlapping method. Ground-level concentrations were measured under 3 conditions with standard deviations of wind directional fluctuation, σA, of 5°, 10° and 20°. From these experimental results, an attempt was made to reduce the general rule of the relation between σA and the maximum ground-level concentration, Cmax over a terrain. The verification and limitation in the application of this rule are discussed. Furthermore, it is reported that large σA has a strong influence on the ground-level concentration patterns and so unexpected concentration patterns appear under some conditions.

The model of the bulk crystallization in a cascade of well-mixed vessels with a continuous removal of solid particles and a recycle is suggested. The system of integro-differential equations describing dynamics of the crystal size distribution density and the supersaturation in apparatuses composing the cascade is obtained. Characteristics of neutral stability of stationary crystallization processes as well as self-oscillating regimes originating as a result of instability are studied in detail. An opportunity for application of external periodic influences for changing conditions of the stability break and for improving the technological characteristics of crystallizers is revealed.

Option to leave is a double-edged sword in the repeated prisoner’s dilemma paradigm. We first show that too much breakup is not necessary in subgame perfect equilibrium distribution. We demonstrate on examples of well-known cooperation inducing solutions that, once an invasion with mixed behavior strategy is allowed in the definition of neutrally stable distribution, breakups on equilibrium path may invite secret-handshake type of invasions.

The present paper is concerned with the long-standing selection problem of the tip velocity in dendritic growth. Based on the global stability analysis of the system, a global neutral stability (GNS) condition of dendritic growth is proposed, which determines the tip velocity and the pattern formation. The theoretical predictions show a good agreement with the experimental investigations.

An agent with a misperception may have an evolutionary advantage when others recognize his misperception and its behavioral implications. In such situations evolutionary forces can lead to misperceptions, yielding "irrational behavior," such as the play of strictly dominated strategies. We point out that this reasoning relies on the assumption of subjective rationality-agents are assumed to choose the behavior that maximizes their perceived payoffs. However, subjective rationality does not have solid evolutionary foundations: in the presence of misperceptions, agents who do not maximize their perceived payoffs may have greater fitness than those who do. We show that relaxing the subjective rationality requirement, somewhat paradoxically, leads to effectively rational behavior: although agents may have systematic misperceptions, they will develop other biases to undo these misperceptions, and will act as if they are rational. As a result, systematic biases in experimental settings may not necessarily translate into irrational behavior. We also demonstrate that the same evolutionary forces, in the long run, lead agents to play as if they have a common prior, even though each agent will have different and possibly incorrect perceptions of payoffs and the rules of the game.

Observations show that the increase in speed as wind blows over a low hill of length L varies with stability in a way which supports the role of the Jackson and Hunt (1975) reference velocity uL in determining the surface pressure perturbation. Speed-up tends to become constant with increasing stability, due to the limiting effect of the shallow nocturnal boundary layer. The magnitude of speed-up at neutral stability is well predicted when the hill shape factor is properly specified. There are significant effects on speed-up due to surface roughness and angle of incidence to the ridge.

The predator-prey systems of Lotka and Volterra are modified to include efficiencies e ij of converting prey biomass to predator biomass. For three or more species, it is shown that neutral stability results if e ik = e ij e jk for all transfers. When the number of species is odd, consistency of the differential equation system for changes in logarithms of biomass is also required.

Full-scale data from two sources, structural damage to the East Side Water Catchment and a survey of turbulence on the approach flightpath to the airfield at Gibraltar, are compared with the results of wind-tunnel tests on a scale model of the Rock. The comparisons show that wind-tunnel simulation of the flow around large sharp-edged topographical features is practical at scale factors as high as 1 5000 for conditions of strong wind and neutral stability. The Rock is shown to behave as one half of a narrow-delta lifting body on an infinite ground plane.

The neutral stability criteria for the generalized case of flow due to circumferential pumping and rotation of the inner cylinder are reviewed. The neutral stability is defined by the parameter, P , as used by B rewster . Heat transfer data taken from the literature have been recalculated. The parameter P is found to be useful in correlating the data.