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
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero