The variational method of coupled Gaussian functions is applied to Bose-Einstein condensates with long-range interactions. The time dependence of the condensate is described by dynamical equations for the variational parameters. We present the method and analytically derive the dynamical equations from the time-dependent Gross-Pitaevskii equation. The stability of the solutions is investigated ...

Consider a continuous dynamical system for which partial information about its current state is observed at a sequence of discrete times. Discrete data assimilation inserts these observational measurements of the reference dynamical system into an approximate solution by means of an impulsive forcing. In this way the approximating solution is coupled to the reference solution at a discrete sequ...

In literature many chaotic systems, based on third-order jerk equations with different nonlinear functions, are available. A jerk system is taken to be a part of dynamical systems that can exhibit regular and chaotic behavior. By extension, a hyperjerk system can be described as a dynamical system with nth-order ordinary differential equations where n is 4 or up to. Hyperjerk systems have been ...

1 Outline In this article we give an overview of the application of theories from dynami-cal systems to the analysis of numerical methods for initial-value problems. We start by describing the classical viewpoints of numerical analysis and of dynami-cal systems and then indicate how the two viewpoints can be merged to provide a framework for both the interpretation of data obtained from numeric...

We consider the (n 1)-dimensional Lotka-Volterra system (arising in biological modelling of species interactions), and associate with it a family of n-dimensional systems having the same phase portrait. We obtain some results on global behaviour and convergence towards the equilibrium in the case where the LV system is “nearly symmetric” or “nearly cooperative” (that is, there exists a member o...

In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c∗, and show the existence of traveling plane wave solutions conn...

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