Sign Of Speed Research Articles

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 traveling waves in degenerate competitive systems

This article studies the bistable traveling wave solutions for diffusion-competition systems, in which the degenerate nonlinearities appear and two different diffusion modes are admissible. The corresponding reaction system has two locally asymptotically stable steady states and two unstable steady states. Using the abstract theory established for monotone semiflows, we obtain the existence of monotone bistable traveling wave solutions. The uniqueness of wave speed is confirmed by constructing appropriate upper and lower solutions. When the initial value satisfies proper conditions, it is proved that the wave speed is the expansion speed of two functions defined by the corresponding Cauchy problem, which implies that the sign of wave speed determines the relative competitiveness in population dynamics. Numerically, it seems that the species with stronger degeneracy may have stronger competitiveness under bistable assumption and other proper conditions.

The monotone traveling wave solution of a bistable three-species competition system via unconstrained neural networks.

In this paper, we approximate traveling wave solutions via artificial neural networks. Finding traveling wave solutions can be interpreted as a forward-inverse problem that solves a differential equation without knowing the exact speed. In general, we require additional restrictions to ensure the uniqueness of traveling wave solutions that satisfy boundary and initial conditions. This paper is based on the theoretical results that the bistable three-species competition system has a unique traveling wave solution on the premise of the monotonicity of the solution. Since the original monotonic neural networks are not smooth functions, they are not suitable for representing solutions of differential equations. We propose a method of approximating a monotone solution via a neural network representing a primitive function of another positive function. In the numerical integration, the operator learning-based neural network resolved the issue of differentiability by replacing the quadrature rule. We also provide theoretical results that a small training loss implies a convergence to a real solution. The set of functions neural networks can represent is dense in the solution space, so the results suggest the convergence of neural networks with appropriate training. We validate that the proposed method works successfully for the cases where the wave speed is identical to zero. Our monotonic neural network achieves a small error, suggesting that an accurate speed and solution can be estimated when the sign of wave speed is known.

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.

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.

Sign of the pulsating wave speed for the bistable competition–diffusion system in a periodic habitat

Sign of the pulsating wave speed for the bistable competition–diffusion system in a periodic habitat

Cosmological analysis of noninteracting and interacting generalized ghost dark energy in Einstein–Aether gravity theory

We have investigated the generalized QCD ghost model of dark energy (DE) in the framework of Einstein–Aether gravity. At first we have discussed the noninteracting generalized ghost DE (GGDE) model in flat Friedmann–Robertson–Walker (FRW) universe and then we have generalized the discussion to the interacting GGDE model in flat and nonflat universe. According to this, we have analyzed the nature of the equation of state (EoS) parameter, deceleration parameter and slow-roll parameters. We have used the sign of square speed of sound to determine the stability of the model in different cases. Also, we have analyzed [Formula: see text] plane in graphically and pointed out freezing region and thawing region in that plane. Then we enlarge our discussion to verify the effectiveness of this model under investigation by analyzing the statefinder diagnosis parameters for the present cosmological setup. The nature of slow-roll parameters in both scenarios with and without interactions has been shown diagrammatically.

Speed sign of traveling waves to a competitive Lotka-Volterra recursive system with bistable nonlinearity

<p style='text-indent:20px;'>Traveling wave propagation is a significant phenomenon observed in population biology. Due to the occurrence of nonlocal effect in recursive systems, a deep understanding of the wavefront in the propagation direction (speed sign) is challenging. In this paper we study the sign of wave speed for bistable traveling waves to a two-species competitive system that biologically models the dynamics of two species in competition for a common resource. By a proper choice of the kernel functions, we transfer our model into a coupled localized differential system and shed a new light on how to determine the wave speed sign. Sufficient conditions with symmetry are obtained on the propagation directions of the wavefronts. This symmetry is further verified in the final analysis and numerical simulations are provided to illustrate our theoretical results.</p>

Artistic Resources of Punctuation in V.V. Nabokov’s Works: from Linguistic to Figurative Sign

The article examines the artistic resources of punctuation marks in V.V. Nabokov’s works. It is known that the writer closely monitored the preservation of the author's punctuation in the translations of his books and left judgments about Flaubert’s punctuation as a significant stylistic feature. The writer's repeated reference to punctuation marks as a source of metaphors allows us to talk about the semantics of signs. The article focuses on the works of Nabokov, created in two languages and belonging to all three modes of literature. The possibility of considering English-language works together with those written in Russian is due to the mutual interference of the principles of punctuation and the very output of the graphic system beyond the purely linguistic level. The article examines the use of ellipsis, dashes, brackets and exclamation marks as elements of a figurative system rather than punctuation (based on syntax). So, the use of ellipsis and less often dashes is stable to indicate the non-verbalized essence of being, the underside of life. Brackets are associated with the sphere of theatricality in a broad sense, they mark the claims of the characters to authorship in their own lives. It is possible to use brackets to separate several narrative streams. There are cases when the inclusion of the meta description of the sign does not agree with the punctuation that forms these fragments. Such cases indicate the unreliability of the narrator. A special phenomenon is the iconic use of punctuation marks, when their semantic parameters are set by a graphic appearance. For example, the ellipsis visually resembles the traces left, and the brackets are a circle. The dash becomes a visible sign of speed, vector of movement or connection, internal kinship. The considered material allows us to see in Nabokov’s punctuation marks units that have their own semantics, relatively stable throughout the author’s work. We stipulate that this position cannot be applied to every use of the punctuation mark. The cases when punctuation marks become elements of the figurative, and not only the linguistic level, are individualized and determined by the broad context of the work.

Propagation dynamics of an anisotropic nonlocal dispersal equation with delayed nonlocal response

This paper focuses on the critical wave speed and the traveling wave fronts for a general anisotropic nonlocal dispersal equation with delayed nonlocal response. Unlike most of the previous study, both of the dispersal kernel function and the nonlocal response function are asymmetric in such an equation. By analyzing the properties of eigenfunction, we first discuss the sign of the critical wave speed and the influence of the asymmetry of the two kernel functions on the critical wave speed. Then under the monostable condition, by using super- and subsolution and monotone iteration method, we obtain the existence of nondecreasing traveling wave solution for c>c∗ and a limiting argument for c=c∗. Moreover, we depict the asymptotic behavior of the traveling wave and its derivative at minus infinity.

Passivity Guaranteed Dynamic Friction Model With Temperature and Load Correction: Modeling and Compensation for Collaborative Industrial Robot

In this paper, a new comprehensive dynamic friction model for a collaborative industrial robot joint that considers the velocity, temperature, and load torque is proposed. The variation of load-dependent friction among the four-quadrant operation depending on the sign of load-torque and speed is studied. The new model’s passivity property is analyzed to obtain a physically meaningful and experimentally identified friction model. A sufficient condition is presented in terms of a simple algebraic inequality involving the parameters of the model. The model parameter identification procedure and validation of model effectiveness are demonstrated experimentally on a commercial collaborative robot manipulator. Moreover, the proposed friction model’s benefits are demonstrated in two different robot applications: friction compensation and direct teaching (smooth lead-through programming) applications. Significant tracking performance improvement in the root-mean-square errors up to 76% was achieved with the proposed friction model compared to the uncompensated cases in the friction compensation application. In the direct teaching application, the new model, which precisely estimates joint friction, results in a significant decrease in interaction forces up to 66%. These experimental results validate the performance of the proposed friction model.

Propagation Direction of the Traveling Wave for the Lotka–Volterra Competitive Lattice System

In this paper, the speed sign of the traveling wave to the bistable Lotka–Volterra competitive lattice system is investigated via the upper–lower solution method as well as the comparison principle. We provide an interval estimation for the bistable speed firstly. Two comparison principles are further established to obtain new conditions to the determinacy of the sign of the bistable speed. To our knowledge, this is the first investigation to the lattice system for the propagation direction.

Bistable wave speed of the Lotka-Volterra competition model

This work deals with the speed sign of travelling waves to the Lotka-Volterra model with diffusion and bistable nonlinearity. We obtain new conditions for the determinacy of the sign of the bistable wave speed by constructing upper or lower solutions with an inside parameter to be adjusted. The established conditions improve or supplement the results in the references and give insight into the combined effect of system parameters on the propagation direction of the bistable wave.

The sign of traveling wave speed in bistable dynamics

We are concerned with the sign of traveling wave speed in bistable dynamics. This question is related to which species wins the competition in multiple species competition models. It is well-known that the wave speed is unique for traveling wave connecting two stable states. In this paper, we first review some known results on the sign of wave speed in bistable two species competition models. Then we derive rigorously the sign of bistable wave speed for a special three species competition model describing the competition in two different circumstances: (1) two species are weak competitors and one species is a strong competitor; (2) three species are very strong competitors. It is interesting to observe that, under certain conditions on the parameters, two weaker competitors can wipe out the strongest competitor.

Global continuation of monotone waves for bistable delayed equations with unimodal nonlinearities

We study the existence of monotone wavefronts for a general family of bistable reaction–diffusion equations with delayed reaction term g. Differently from previous works, we do not assume the monotonicity of with respect to the delayed variable that does not allow to apply the comparison techniques. Thus our proof is based on a variant of the Hale–Lin functional-analytic approach to heteroclinic solutions of functional differential equations where Lyapunov–Schmidt reduction is done in appropriate weighted spaces of C2-smooth functions. This method requires a detailed analysis of associated linear differential operators and their formal adjoints. For two different types of -unimodal functions , we establish the existence of a maximal continuous family of bistable monotone wavefronts. Depending on the type of unimodality (equivalently, on the sign of the wave speed), two different scenarios can be observed for the obtained bistable waves: (1) independently on the size of delay, each bistable wavefront is monotone; (2) wavefronts are monotone for moderate values of delays and can oscillate for large delays.

Cosmological evolution for magnetic universe based in a simple nonlinear electrodynamics

We investigate the cosmic dynamics of Friedmann-Robertson-Walker universes – flat spatial sections – which are driven by nonlinear electrodynamics (NLED) Lagrangian. We pay special attention to the check of the sign of the square sound speed since, whenever the latter quantity is negative, the corresponding cosmological model is classically unstable against small perturbations of the background energy density. Besides, based on causality arguments, one has to require that the mentioned small perturbations of the background should propagate at most at the local speed of light. We also look for the dynamics by mean of dynamical system tools. Our results indicate that in the case of the power law NLED Lagrangian, it is not possible to explain the current accelerated expansion stage of the universe because the model is not stable for the possible values of the free parameter that allows such expansion. Finally, in the second case, whose Lagrangian has a power law NLED term plus a Maxwell term, the model is stable and causal for a certain range of values of the free parameter.

Indirect Control of Oscillations: Elements of Theory

A brief review of the main research areas in the field of controlled vibration protection systems is given. It is shown that Vibration systems with indirect control processes of oscillations allow with a minimum expenditure of energy to ensure programmable switching parameters and structures, in which the dissipative restoring and inertial forces generated on the basis of active impact. Within synthesis of indirect control the chains of new auxiliary mathematical constructs for finding optimal synthesizing functions of the elastic-damping units parameters control are obtained. It enabled to separate a base model with intermittent damping and base model with impulse trap. As a result of the study, based on the harmonic balance method, the dynamic properties of the basic model with intermittent damping, calculation formulas are obtained for determining the parameters of the compensation effect and calculating the dynamic coefficient. It is established that, with an optimal sequence of damping switching, the resonant phenomena are eliminated, and the transient processes decay within one period of the kinematic perturbation. The basic model with a pulse trap imitates the limiting variant of intermittent damping and realizes the process of superimposing constraining bonds, the sequence and duration of which are new variables essentially increasing controllability. And for indirect pulse control, there exicts a certain minimum of power consumption independent of the achieved effect of vibration protection. A regulated increase in the duration of the application of the restraining coupling in the low-frequency region and a decrease in this duration in the high-frequency region provides a monotonically decreasing dependence on the dynamic coefficients over the entire frequency range. An example of a solution to the optimization problem of controlling the damping process for a basic model of a vibration isolation system is considered. It is established that intermittent damping is an indispensable feature of the optimality of the vibration isolation system: the damper switches on when the sign of the object's speed has changed and turns off when the object's displacement sign has changed.

A Game-Theoretic Analysis of Cyber Switching Attacks and Mitigation in Smart Grid Systems

We propose a framework for the analysis of cyber switching attacks and control-based mitigation in cyber-enabled power systems. Our model of the switching attack is simple, only requiring knowledge of the sign of the local relative rotor speed, which may be estimated. The controller is modeled to be resource constrained, choosing to act only during select intervals of time. We make use of an iterated game-theoretic formulation to describe the interactions of the parties and its effect on system stability. Analytic results indicate the potential of the constrained controller to achieve transient stabilization over time using zero-determinant strategies. Numerical results of the New England 39-bus power system demonstrate the potential for such a controller to increase system resilience during cyber-attacks.

Can zonally symmetric inertial waves drive an oscillating zonal mean flow?

In the present paper zonal mean flow excitation by inertial waves is studied in analogy to mean flow excitation by gravity waves that plays an important role for the quasi-biennial oscillation in the equatorial atmosphere. In geophysical flows that are stratified and rotating, pure gravity and inertial waves correspond to the two limiting cases: gravity waves neglect rotation, inertial waves neglect stratification. The former are more relevant for fluids like the atmosphere, where stratification is dominant, the latter for the deep oceans or planet cores, where rotation dominates. In the present study a hierarchy of simple analytical and numerical models of zonally symmetric inertial wave-mean flow interactions is considered and the results are compared with data from a laboratory experiment. The main findings can be summarised as follows: (i) when the waves are decoupled from the mean flow they just drive a retrograde (eastward) zonal mean flow, independent of the sign of the meridional phase speed; (ii) when coupling is present and the zonal mean flow is assumed to be steady, the waves can drive vertically alternating jets, but still, in contrast to the gravity wave case, the structure is independent of the sign of the meridional phase speed; (iii) when coupling is present and time-dependent zonal mean flows are considered the waves can drive vertically and temporarily oscillating mean flows. The comparison with laboratory data from a rotating annulus experiment shows a qualitative agreement. It appears that the experiment captures the basic elements of the inertial wave mean flow coupling. The results might be relevant to understand how the Equatorial Deep Jets can be maintained against dissipation, a process currently discussed controversially.