Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 224
... sharks and the small fish consumed by the sharks . ( Another predator - prey situation , frequently investigated in mathematics texts , describes the ecosystem of foxes and rabbits . ) Let number of a certain species of F = fish ( eaten ...
... sharks and the small fish consumed by the sharks . ( Another predator - prey situation , frequently investigated in mathematics texts , describes the ecosystem of foxes and rabbits . ) Let number of a certain species of F = fish ( eaten ...
Page 226
... sharks . The sharks behave in an entirely different manner . If there are no fish , then the food source of the sharks is nonexistent . In this case , the death rate of the sharks is expected to exceed the birth rate . Hence in the ...
... sharks . The sharks behave in an entirely different manner . If there are no fish , then the food source of the sharks is nonexistent . In this case , the death rate of the sharks is expected to exceed the birth rate . Hence in the ...
Page 228
... sharks . ( S > a / c ) the 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 ...
... sharks . ( S > a / c ) the 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 ...
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