Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 224
... fishing for the small plankton - eating fish for a couple of years ( as occurred during World War I ) , then these fish might be expected to increase in number . Once having increased , the sharks would have enough food to sustain a ...
... fishing for the small plankton - eating fish for a couple of years ( as occurred during World War I ) , then these fish might be expected to increase in number . Once having increased , the sharks would have enough food to sustain a ...
Page 226
... fish ceases at some large population , then a logistic growth model might be proposed , dF dt = aFbF2 . = Thus , the rate of population change of the fish , dF / dt = g ( F , S ) , is such that g ( F , 0 ) is given by either g ( F , 0 ) ...
... fish ceases at some large population , then a logistic growth model might be proposed , dF dt = aFbF2 . = Thus , the rate of population change of the fish , dF / dt = g ( F , S ) , is such that g ( F , 0 ) is given by either g ( F , 0 ) ...
Page 228
... fish population diminishes . If at some time the sharks number exactly S = a / c , then at that time the fish population does not vary . This level of sharks depends on a , the growth rate of the fish in the absence of sharks and c ...
... fish population diminishes . If at some time the sharks number exactly S = a / c , then at that time the fish population does not vary . This level of sharks depends on a , the growth rate of the fish in the absence of sharks and c ...
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 |
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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