Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 185
... Species Models In the previous sections , different models of the population growth of a single species were discussed . In an attempt to understand large ecosystems , we will study situations that involve the interaction of more than ...
... Species Models In the previous sections , different models of the population growth of a single species were discussed . In an attempt to understand large ecosystems , we will study situations that involve the interaction of more than ...
Page 186
... species , their respective populations being N1 and N2 . As in the mathematical models of single species ecosystems , we assume that the rates of change of each species depend only on the populations of each species , not other ...
... species , their respective populations being N1 and N2 . As in the mathematical models of single species ecosystems , we assume that the rates of change of each species depend only on the populations of each species , not other ...
Page 247
... Species Not all species form predator - prey relationships . In this section we will investigate a two - species ecosystem in which both species compete for the same limited source of nutrients . In deriving the governing system of ...
... Species Not all species form predator - prey relationships . In this section we will investigate a two - species ecosystem in which both species compete for the same limited source of nutrients . In deriving the governing system of ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero