Search results for "Equilibrium"
showing 10 items of 1021 documents
An upper bound of the index of an equilibrium point in the plane
2012
Abstract We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index.
Planar systems with critical points: multiple solutions of two-point nonlinear boundary value problems
2005
Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. First, we consider the planar systems equivalent to equation x ″ = f ( x ) , where f ( x ) has multiple zeros and the respective system has centers and saddle points in various combinations. Estimations of the number of solutions are given. Then results are extended to nonautonomous equations which have superlinear behavior at infinity.
An equilibrium point regularization for the Chen system
2006
This paper addresses the control of the chaotic Chen system via a feedback technique. We first present a nonlinear feedback controller which drives the trajectories of the Chen system to a given point for any initial conditions. Then, we design a linear feedback controller which still assures the global stability of the Chen system. We moreover achieve the tracking of a reference signal. Numerical simulations are provided to show the effectiveness of the developed controllers.
Smooth and non-smooth traveling wave solutions of some generalized Camassa–Holm equations
2014
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of three of the GCH NLPDEs, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do not support singular traveling waves. The third equation supports four-segmented, non-smooth $M$-wave solutions, while the fourth supports both solitary (peakon) and periodic (cuspon) cusp waves in different parameter regimes. Moreover, sm…
Improving Pairs Trading Using Neural Network Techniques and Fundamental Ratios
2020
Pairs trading is a quantitative trading strategy consisting on identifying two stocks that historically move together and, using the assumption that their prices difference has mean- reverting properties, exploit the deviation from the mean by taking long – short position in the chosen pair to profit. Throughout the years, different approaches have been developed in order to exploit this strategy. However, there is little literature who looks whether the divergences in the prices are generated by poor company results, i.e. whether the deviation from the mean are product of bad (or good) fundamentals and are justified, or if they generate a new equilibrium point for the pair. In addition, si…
Probabilistic stability analysis of social obesity epidemic by a delayed stochastic model
2014
Abstract Sufficient conditions for stability in probability of the equilibrium point of a social obesity epidemic model with distributed delay and stochastic perturbations are obtained. The obesity epidemic model is demonstrated on the example of the Region of Valencia, Spain. The considered nonlinear system is linearized in the neighborhood of the positive point of equilibrium and a sufficient condition for asymptotic mean square stability of the zero solution of the constructed linear system is obtained.
On basins of attraction for a predator-prey model via meshless approximation
2016
Abstract. In this work an epidemiological predator-prey model is studied. It analyzes the spread of an infectious disease with frequency-dependent and vertical transmission within the predator population. In particular we consider social predators, i.e. they cooperate in groups to hunt. The result is a three-dimensional system in which the predator population is divided into susceptible and infected individuals. Studying the dynamical system and bifurcation diagrams, a scenario was identified in which the model shows multistability but the domain of attraction of one equilibrium point can be so small that it is almost the point itself. From a biological point of view it is important to anal…
Evolutionary Game Dynamics for Collective Decision Making in Structured and Unstructured Environments
2017
Abstract For a large population of players we consider a collective decision making process with three possible choices: option A or B or no option. The more popular option is more likely to be chosen by uncommitted players and cross-inhibitory signals can be sent to attract players committed to a different option. This model originates in the context of honeybees swarms, and we generalise it to accommodate other applications such as duopolistic competition and opinion dynamics. The first contribution is an evolutionary game model and a corresponding new game dynamics called expected gain pairwise comparison dynamics explaining how the strategic behaviour of the players may lead to deadlock…
Regular and singular pulse and front solutions and possible isochronous behavior in the short-pulse equation: Phase-plane, multi-infinite series and …
2014
In this paper we employ three recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a family of so-called short-pulse equations (SPE). A recent, novel application of phase-plane analysis is first employed to show the existence of breaking kink wave solutions in certain parameter regimes. Secondly, smooth traveling waves are derived using a recent technique to derive convergent multi-infinite series solutions for the homoclinic (heteroclinic) orbits of the traveling-wave equations for the SPE equation, as well as for its generalized version with arbitrary coefficients. These correspond to pulse (kink or shock) solutions respectively o…
Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere
2006
We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15