Stability Analysis Of Equilibrium Points Research Articles

Effects of system parameter and fractional order on dynamic behavior evolution in fractional-order Genesio-Tesi system

The object of this paper is to reveal the relationship between dynamics of the fractional-order Genesio-Tesi system and its parameter, especially the order of fractional derivatives. At first, the transcritical bifurcation is carried out based on the stability analysis of equilibrium points. Then, effects of system parameter and fractional order on the dynamics have been investigated deeply and systematically. For commensurate fractional-order system, period-doubling bifurcation, reverse period-doubling bifurcation, period window, transient chaos and steady chaos are found with parameter and fractional order varying simultaneously. For incommensurate fractional-order system, there also exists the route to chaos by period-doubling bifurcation. Furthermore, the effect of different fractional orders on dynamical behavior evolution has been compared. These new findings contribute to successful selecting the most efficient control function, which has been validated by some numerical tools.

Bifurcation analysis of a single-group asset flow model

We study the stability and Hopf bifurcation analysis of an asset pricing model that based on the model introduced by Caginalp and Balenovich in 1999, under the assumption of a xed amount of cash and stock in the system. First, we study stability analysis of equilibrium points. Choosing the momentum coe¢ cient as a bifurcation parameter, we also show that Hopf bifurcation occurs when the bifurcation parameter passes through a critical value. Analytical results are supported by numerical simulations. A key conclusion for economics and nance is the existence of periodic solutions for an interval of the bifurcation parameter, which is the trend-based (or momentum) coe¢ cient. Key words. Asset price dynamics, stability of price dynamics, Hopf bifurcation, price trend, momentum, market dynamics, liquidity, periodic solutions. AMS subject classi cation. : 91B25, 91B26, 91B50, 91G80, 91G99, 34D20, 34C60, 37G15, 37N40 1. Introduction. A central theme in classical nance is that market participants all have access to the same information, and all seek to optimize their returns so that a unique equilibrium price is established (see, for example, [3], [18], [20]). The approach to equilibrium is often assumed to be a process involving some randomness or noise, but otherwise smooth and rapid. Aside from noise, one can expect that prices will not overshoot the equilibrium price since the equation governing the change in price, P , is a rst order in time, i.e., P 0 = F (D=S) where S and D are supply and demand that depend on price but not on the recent price derivative history. As such, there is no mechanism for oscillations or cyclic behavior within this setting. A well known example of cyclic behavior in economics is called the cobweb theorem whereby prices oscillate periodically due to the time lag between supply and demand decisions. Agricultural commodities provide a simple example with a delay between planting and harvesting (see [21] (pages 133-134 gives two agricultural examples: rubber and corn) and [36]). In nancial markets, however, the prevailing theory (at least during latter part of the 20th century), called the e¢ cient market hypothesis (EMH), maintains the existence of in nite arbitrage capital that would quickly exploit any deviations between the trading price and the intrinsic or fundamental value of the asset, which are necessarily unique since the participants have the same information and calculation of future returns. The absence of any delay in information or trading excludes, mathematically, the possibilities of overshooting the equilibrium price or oscillating about it. While policy makers often discuss instabilities in asset prices, classical nance tends to treat these as rare occurrences within a stochastic setting. In particular, much of classical nance is based on the concept that an asset’s price, P (t), is governed by Current address: Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA. Permanent address: Department of Mathematics, TOBB University of Economics and Technology, 06560-Ankara, TURKEY. H. Merdan was supported by TUBITAK (The Scienti c and Technological Research Council of Turkey) yDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA zDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

On stability of equilibrium points in nonlinear fractional differential equations and fractional Hamiltonian systems

In this article, a brief stability analysis of equilibrium points in nonlinear fractional order dynamical systems is given. Then, based on the first integral concept, a definition of planar Hamiltonian systems with fractional order introduced. Some interesting properties of these fractional Hamiltonian systems are also presented. Finally, we illustrate two examples to see the differences between fractional Hamiltonian systems with their classical order counterparts.© 2014 Wiley Periodicals, Inc. Complexity 21: 93–99, 2015

On the Stability of Delay Population Dynamics Related with Allee Effects

In recent years, many scientists have focus on the studies of the Allee effect in population dynamics. This paper presents the stability analysis of equilibrium points of population dynamics with Allee effect which occurs at low population density.

Characteristic analysis of hydraulic hybrid vehicle based on limit cycle

The theory of limit cycles was applied to hydraulic hybrid vehicle (HHV) to analyze the dynamic characteristics of the system. The exact mathematical models based on configuration diagram of HHV were built to study on equilibrium points, nonexistence of limit cycle and stability of equilibrium points. The analysis showed that if the Young’s modulus of fluid is neglected, the equilibrium points of the system will be distributed on both sides of the initial function. In addition, there is a unique equilibrium point according to the practical signification of the system parameters. The nonexistence analysis showed that there is no limit cycle for the system, no matter how the viscosity coefficient B changes. The stability analysis of equilibrium points showed that the system is asymptotically stable about the equilibrium point at B⩾0 and the equilibrium point is the center point of the system at B=0. Finally, the phase diagrams of global topological structure of HHV system were entirely described according to qualitative analysis of the singular points at infinity.

A Mathematical Study of a Predator-Prey Dynamics with Disease in Predator

We consider a predator-prey model where parasitic infection is spread in only predator population. We work out the local stability analysis of equilibrium point by the help of basic reproduction numbers. We also analyze the community structure of model system by the help of ecological as well as disease basic reproduction numbers. We derive Hopf bifurcation condition and permanence and impermanence of model system. We perform a numerical experiment and observe that parasitic infection in predator population stabilizes predator-prey oscillations.

Stability analysis of continuous population model involving predation and Allee effect

This paper presents the stability analysis of equilibrium points of a general continuous time population dynamics model involving predation subject to an Allee effect which occurs at low population density. The mathematical results and numerical simulations show that the system subject to an Allee effect takes much longer time to reach its stable state at an equilibrium point at which is indeed stable.

On the stability analysis of a general discrete-time population model involving predation and Allee effects

This paper presents the stability analysis of equilibrium points of a general discrete-time population dynamics involving predation with and without Allee effects which occur at low population density. The mathematical analysis and numerical simulations show that the Allee effect has a stabilizing role on the local stability of the positive equilibrium points of this model.

Allee effects on population dynamics in continuous (overlapping) case

This paper presents the stability analysis of equilibrium points of a continuous population dynamics with delay under the Allee effect which occurs at low population density. The mathematical results and numerical simulations show the stabilizing role of the Allee effects on the stability of the equilibrium point of this population dynamics.

Study on Discrete Time Mapping Modeling and Stability Analysis for Piecewise Autonomous Oscillation Systems

System modeling and local stability analysis of equilibrium points are indispensable for analysis of bifurcation and chaos behaviors observed in piecewise autonomous oscillation system. This paper presents a novel dynamic discrete mapping modeling method and local stability criterion of equilibrium points. This modeling method sets up discrete mapping model and boundary equations in analytic form respectively. With the aid of Newton-Raphson algorithm, the boundary equations can be solved dynamically. Combining the mapping model with boundary dynamic solutions, this mapping model can fulfill the requirements of fast-scale bifurcation analysis. To verify this modeling method, an autonomous oscillation circuit used in power electronics soft switched converter is constructed. A frequency bifurcation phenomenon is captured in both simulation results and experiment system. The analysis results of this bifurcation phenomena show consistency between model simulation and experiment system.

Allee effects on population dynamics with delay

In this paper, we study the stability analysis of equilibrium points of population dynamics with delay when the Allee effect occurs at low population density. Mainly, our mathematical results and numerical simulations point to the stabilizing effect of the Allee effects on population dynamics with delay.

Extension of characteristic equation method to stability analysis of equilibrium points for closed-loop PWM power switching converters

An extension of characteristic equation analysis method to the stability analysis of equilibrium points for closed-loop PWM power switching converters is introduced based on equivalent small parameter method. The basic principle of the method is described in detail. The provided example shows that the method, incorporating with the system's state-plane trajectories, offers the advantages of both simplicity and practicality.

New Results for an Asymmetric Rigid Body with Constant Body-Fixed Torques

The rotational motion of an asymmetric rigid body under the ine uence of constant body-e xed torque is investigated. A set of nondimensional equations of motion is introduced for the stability analysis of equilibrium points. In particular, three-dimensional phase space trajectories are developed for two different cases: 1 ) constant torque along the major or minor axis and 2 ) constant torque along the intermediate axis. For both cases, some new analytical as well as simulation results are presented in terms of equilibrium manifolds, separatrix surfaces, periodic or nonperiodic solutions, and extrema of the periodic solutions.

On the performance of Hopfield network for graph search problem

This paper presents a study on the performance of the Hopfield neural network algorithm for the graph path search problem. Specifically, performance of the Hopfield network is studied from the dynamic systems stability perspective. Simulations of the time behavior of the neural network is augmented with exhaustive stability analysis of the equilibrium points of the network dynamics. The goal is to understand the reasons for the well-known deficiency of the Hopfield network algorithm: the inability to scale up with the problem size. A recent procedure, which establishes solutions as stable equilibrium points in the state space of the network dynamics, is employed to define the constraint weight parameters of the Hopfield neural network. A simulation study of the network and stability analysis of equilibrium points indicate that a large set of non-solution equilibrium points also becomes stable whenever constraint weight parameters are set to make the solution equilibrium points stable. As the problem size grows, the number of stable non-solution equilibrium points increases at a much faster rate than the number of stable solution equilibrium points: the network becomes more likely to converge to a non-solution equilibrium point.

Effect of cortisone in experimental syphilis in rabbits.

<h3>Abstract</h3> In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagin’s Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.