In this paper we focus on a generalized Hénon–Heiles system in a rotating reference frame, in such a way that Lagrangian-like equilibrium points appear. Our goal is to study their nonlinear stability properties to better understand the dynamics around these points. We show the conditions on the free parameters to have stability and we prove the superstable character of the origin for the classi...

We extend a recent investigation by Meehan et al. (2017) [1] regarding the global stability properties of the general Kermack-McKendrick model to the multi-strain case. We demonstrate that the basic reproduction number of each strain R0j represents a sharp threshold parameter such that when R0j ≤ 1 for all j each strain dies out and the infection-free equilibrium is globally asymptotically stab...

Abstract: In this paper we investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved ...

Modified T cells that have been engineered to recognize the CD19 surface marker have recently been shown to be very successful at treating acute lymphocytic leukemias. Here we explore four previous approaches that have used ordinary differential equations to the model this type of therapy, compare their properties, and modify the models to address their deficiencies. Although the four models tr...

This papers examines the structural implications of demand shifts in free-entry oligopoly equilibria. The model generalizes the conjectural variations framework to consider asymmetric firm conjectures, allows for the possibility of cost differences across firms, and endogenizes conditions of entry and exit in the industry. In non-competitive environments, changes in incumbent output and industr...

Background: HIV is a virus that directed at destroying the human immune system thereby exposing body to risk of been affected by other common illnesses and if it not treated, generates more chronic illness called AIDS. Materials Methods: In this paper, we employed fixed-point theory in developing uniqueness existence solution fractional order HIV/AIDS model having Caputo-Fabrizio operator. This...

Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando’s optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermody...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...