Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 144
... occurs or it does not ; there are no other possibilities . In At time , if the probability of one birth from one hen is △ t , then we " expect " if there are a large number of hens No , then there would be No △ t births . This shows ...
... occurs or it does not ; there are no other possibilities . In At time , if the probability of one birth from one hen is △ t , then we " expect " if there are a large number of hens No , then there would be No △ t births . This shows ...
Page 168
... occurs in other cases . In fact , we do not even know if the equilibrium population will always be stable ! - Recall without a delay a population satisfying the logistic differential equation will approach the environment's carrying ...
... occurs in other cases . In fact , we do not even know if the equilibrium population will always be stable ! - Recall without a delay a population satisfying the logistic differential equation will approach the environment's carrying ...
Page 365
... occur immediately . Let us attempt to calculate when a shock first occurs . Suppose that the first shock occurs at t = T , due to the intersection of two characteristics initially a distance Ax ( not necessarily small ) apart , one ...
... occur immediately . Let us attempt to calculate when a shock first occurs . Suppose that the first shock occurs at t = T , due to the intersection of two characteristics initially a distance Ax ( not necessarily small ) apart , one ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
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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