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 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
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analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др