Do part (1) and (3)Homework Answers
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Do part (1) and (3)
• (Problem 1) Given the Lotka-Voltera model: = F(a-cs) dF dt...
(Problem 1) Given the Lotka-Voltera model: -) dF F(a-cs) dt ds S(-k + XF). dt (1)...
(Problem 1) Given the Lotka-Voltera model: -) dF F(a-cs) dt ds S(-k + XF). dt (1) Linearize the model about the equilibrium point (F, S) = (0,0) using Taylor series.
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds...
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS)...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS) dF dt ds dt S(-k + \F). (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b, c, k, 1. Plot the solutions of...
= • (Problem 4) Consider the following alternate predator-prey (Leslie) model: dF F(a – bF –...
= • (Problem 4) Consider the following alternate predator-prey (Leslie) model: dF F(a – bF – cS) dt dS S S(-k +13). dt F Note that the prey model is the same as in the Lotka-Volterra model. However, the predators change in a different manner. Show that if there are many predators for each prey, then the predators cannot cope with the excessive competition for their prey and die off. On the other hand if there are many prey for...
(Problem 3) Consider the following three-species ecosystems: dF F(a – cS) dt ds S(-k + \F...
(Problem 3) Consider the following three-species ecosystems: dF F(a – cS) dt ds S(-k + \F – mG) dt dG G(-e+oS). dt Assume that the coefficients are positive constants. Describe the role each species plays in this ecological system. =
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR d...
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR dt dF dt R2-R)-12RF . What happens to the population of rabbits if the number of foxes is arro? (Use the phase line analysis from Chapter 2) What happens to the population of foxes if the number of rabbits is zero? 3. Using the method of nullclines, draw an approximate...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively,...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
*** I need help with PART F of this problem. Hints are given in other parts...
*** I need help with PART F of
this problem. Hints are given in other parts of the problem and all
information available is given on the worksheet. Please help, thank
you!
The post-synaptic cell at a chemical synapse has the following distribution of ions between the cytosol and the extracellular environment. Consider that the relative permeabilities for Na, K and Cl' are 1, 100 and 50, and that there are no other significant permeabilities, lon Concentration (in mM) Extracellular...
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tan...
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qii,qi2, Oi3. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks are, respectively, qo1,...
(Problem 1) Given the Lotka-Voltera model: -) dF F(a-cs) dt ds S(-k + XF). dt (1) Linearize the model about the equilibrium point (F, S) = (0,0) using Taylor series.
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS) dF dt ds dt S(-k + \F). (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b, c, k, 1. Plot the solutions of...
= • (Problem 4) Consider the following alternate predator-prey (Leslie) model: dF F(a – bF – cS) dt dS S S(-k +13). dt F Note that the prey model is the same as in the Lotka-Volterra model. However, the predators change in a different manner. Show that if there are many predators for each prey, then the predators cannot cope with the excessive competition for their prey and die off. On the other hand if there are many prey for...
(Problem 3) Consider the following three-species ecosystems: dF F(a – cS) dt ds S(-k + \F – mG) dt dG G(-e+oS). dt Assume that the coefficients are positive constants. Describe the role each species plays in this ecological system. =
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR dt dF dt R2-R)-12RF . What happens to the population of rabbits if the number of foxes is arro? (Use the phase line analysis from Chapter 2) What happens to the population of foxes if the number of rabbits is zero? 3. Using the method of nullclines, draw an approximate...
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...
*** I need help with PART F of
this problem. Hints are given in other parts of the problem and all
information available is given on the worksheet. Please help, thank
you!
The post-synaptic cell at a chemical synapse has the following distribution of ions between the cytosol and the extracellular environment. Consider that the relative permeabilities for Na, K and Cl' are 1, 100 and 50, and that there are no other significant permeabilities, lon Concentration (in mM) Extracellular...
The state space model of an interconnected three tank water storage system is given by the following equation -3 1 o 1[hi] dt The heights of water in the tanks are, respectively, hi, h2, hz. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qii,qi2, Oi3. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks are, respectively, qo1,...
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