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- Title
On a system of nonlinear differential equations for the model of totally connected traffic.
- Authors
Buslaev, Alexander P.; Kozlov, Valery V.
- Abstract
In the paper the qualitative properties solutions of the system nonlinear equations, describing one-way movement of particles chain on a line with follower velocity defined by some function of distance from the leader, are researched. In the case when the given function is the velocity of the first particle (leader) in the chain, the model is called a model of leader. If the given function is the velocity of the last particle (outsider), the model is called a model of "shepherd". The sufficient conditions for the existence of the chain with the given constraints on the velocity and acceleration are obtained.
- Subjects
NONLINEAR differential equations; MATHEMATICAL models; MATHEMATICAL functions; EXISTENCE theorems; CONSTRAINTS (Physics)
- Publication
Journal of Concrete & Applicable Mathematics, 2014, Vol 12, Issue 1/2, p86
- ISSN
1548-5390
- Publication type
Article