Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 58
Page 168
... possible for solutions to the discrete logistic equation with a delay . m + 1 α / β X Χ Nm m - 1 m m + 1 m +2 Figure 40-4 Discrete logistic equation with a delay : possible growth beyond the environment's carrying capacity . In the ...
... possible for solutions to the discrete logistic equation with a delay . m + 1 α / β X Χ Nm m - 1 m m + 1 m +2 Figure 40-4 Discrete logistic equation with a delay : possible growth beyond the environment's carrying capacity . In the ...
Page 188
... possible population of both species such that both populations will not vary in time . The births and deaths of species N1 must balance , and similarly those of N2 must balance . Thus an equilibrium population , N1 = N1 , and N2 N2e ...
... possible population of both species such that both populations will not vary in time . The births and deaths of species N1 must balance , and similarly those of N2 must balance . Thus an equilibrium population , N1 = N1 , and N2 N2e ...
Page 232
... possible kinds of " orbits " of the phase plane , as shown in Fig . 50-4 . For example , suppose that the trajectories are as shown in Fig . 50-5 . As drawn , part of one solution curve is spiralling inwards ( as though the populations ...
... possible kinds of " orbits " of the phase plane , as shown in Fig . 50-4 . For example , suppose that the trajectories are as shown in Fig . 50-5 . As drawn , part of one solution curve is spiralling inwards ( as though the populations ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
80 other sections not shown
Other editions - View all
Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
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