scholarly journals Single Peak Solitons for the Boussinesq-Like B(2,2) Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Lina Zhang ◽  
Shumin Li ◽  
Aiyong Chen
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Soliton Solutions ◽  
Single Peak ◽  
Inhomogeneous Boundary Condition

The nonlinear dispersive Boussinesq-like B(2,2) equation utt+(u2)xx−(u2)xxxx=0, which exhibits single peak solitons, is investigated. Peakons, cuspons and smooth soliton solutions are obtained by setting the B(2,2) equation under inhomogeneous boundary condition. Asymptotic behavior and numerical simulations are provided for these three types of single peak soliton solutions of the B(2,2) equation.

ANALYSIS OF THE INFLUENCE OF LANE CHANGING ON TRAFFIC-FLOW DYNAMICS BASED ON THE CELLULAR AUTOMATON MODEL

2011 ◽  
Vol 22 (03) ◽  
pp. 271-281 ◽  
Author(s):  
SHINJI KUKIDA ◽  
JUN TANIMOTO ◽  
AYA HAGISHIMA
Keyword(s):  
Boundary Condition ◽  
Cellular Automaton ◽  
Numerical Simulations ◽  
Traffic Flow ◽  
Flow Dynamics ◽  
Open Boundary ◽  
Open Boundary Condition ◽  
Lane Changing ◽  
Basic Characteristics ◽  
Conventional Models

Many cellular automaton models (CA models) have been applied to analyze traffic flow. When analyzing multilane traffic flow, it is important how we define lane-changing rules. However, conventional models have used simple lane-changing rules that are dependent only on the distance from neighboring vehicles. We propose a new lane-changing rule considering velocity differences with neighboring vehicles; in addition, we embed the rules into a variant of the Nagel–Schreckenberg (NaSch) model, called the S-NFS model, by considering an open boundary condition. Using numerical simulations, we clarify the basic characteristics resulting from different assumptions with respect to lane changing.

scholarly journals Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming Song ◽  
Bouthina S. Ahmed ◽  
Anjan Biswas
Keyword(s):  
Finite Difference ◽  
Numerical Simulations ◽  
Power Law ◽  
Soliton Solution ◽  
Bifurcation Analysis ◽  
Soliton Solutions ◽  
Phase Portraits ◽  
Zakharov Equation ◽  
Topological Soliton ◽  
Klein Gordon

This paper addresses the Klein-Gordon-Zakharov equation with power law nonlinearity in (1+1)-dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

scholarly journals Asymptotic Behavior Analysis for a Three-Species Food Chain Stochastic Model with Regime Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Junmei Liu ◽  
Yonggang Ma
Keyword(s):  
Asymptotic Behavior ◽  
Lyapunov Function ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Behavior Analysis ◽  
Food Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stationary Distributions ◽  
Theoretical Results

This paper discusses the asymptotic behavior of a class of three-species stochastic model with regime switching. Using the Lyapunov function, we first obtain sufficient conditions for extinction and average time persistence. Then, we prove sufficient conditions for the existence of stationary distributions of populations, and they are ergodic. Numerical simulations are carried out to support our theoretical results.

scholarly journals A lubricant boundary condition for a biological body lined by a thin heterogeneous biofilm

2019 ◽  
Vol 12 (01) ◽  
pp. 1950003
Author(s):  
Mustapha El Jarroudi ◽  
Riane Hajjami ◽  
Aadil Lahrouz ◽  
Moussa El Jarroudi
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Slip Boundary Condition ◽  
The Body ◽  
Local Problem ◽  
Viscous Fluid Flow ◽  
Slip Boundary ◽  
Varying Thickness ◽  
Cellular Microstructure ◽  
Biological Particle

We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure, varying thickness, and a heterogeneous viscosity regulated by a time random process. Letting the thickness of the film tend to zero, we derive an effective biological slip boundary condition on the boundary of the body. This law relates the tangential fluxes to the tangential velocities via a proportional coefficient corresponding to the energy of some local problem. This law describes the ability of the biological film to function as a lubricant reducing friction at the wall of the body. The tangential velocities are functions of the random trajectories of a finely concentrated biological particle.

A Stochastic Model with Saturation Infection for Internal HIV Dynamics

2015 ◽  
Vol 713-715 ◽  
pp. 1546-1551 ◽  
Author(s):  
Jin Qiang Wang ◽  
Mao Xing Liu
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Model ◽  
Numerical Simulations ◽  
Infection Rate ◽  
Virus Dynamics ◽  
Hiv Dynamics

In this paper, a stochastic model with a saturation infection rate representing HIV internal virus dynamics is investigated. We prove that the model exists non-negative solutions. Then we analyse the asymptotic behavior of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

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