1.11.1 In the following circumstances, compute ...and state whether the heart will beat. ...
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1.11.2 In the following circumstances, compute ...and state whether the heart will beat. ...
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1.11.3 In the following circumstances, compute ...and state whether the heart will beat. ...
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1.11.4 In the following circumstances, compute ...and state whether the heart will beat. ...
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1.11.5 Describe
the long-term dynamics in each of the given cases. Find which ones will
beat every time, which display 2:1 AV block, and which show some sort
of Wenckebach phenomenon. The case in Exercise 1. Exercise 1 ...
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1.11.6 Describe
the long-term dynamics in each of the given cases. Find which ones will
beat every time, which display 2:1 AV block, and which show some sort
of Wenckebach phenomenon. The case in Exercise 2. Exercise 2. ...
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1.11.7 Describe
the long-term dynamics in each of the given cases. Find which ones will
beat every time, which display 2:1 AV block, and which show some sort
of Wenckebach phenomenon. The case in Exercise 3. Exercise 3. ...
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1.11.8 Describe
the long-term dynamics in each of the given cases. Find which ones will
beat every time, which display 2:1 AV block, and which show some sort
of Wenckebach phenomenon. The case in Exercise 4. Exercise 4. ...
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1.11.9 Use the parameter values in Exercise 1 (except for the values of c), and state whether the heart would beat every time with the given values of α and τ . α = 1.0, τ = 1.0. Exercise 1 ...
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1.11.10 Use the parameter values in Exercise 1 (except for the values of c), and state whether the heart would beat every time with the given values of α and τ . α = 1.0, τ = 0.5. Exercise 1 ...
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1.11.11 Use the parameter values in Exercise 1 (except for the values of c), and state whether the heart would beat every time with the given values of α and τ . α = 2.0, τ = 0.5. Exercise 1 ...
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1.11.12 Use the parameter values in Exercise 1 (except for the values of c), and state whether the heart would beat every time with the given values of α and τ . α = 0.5, τ = 0.5. Exercise 1 ...
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1.11.13
Consider the following continuous system that approximates the
discontinuous model studied in this chapter ... for the
following values of n. Find the equilibria and their stability as a function of c, and describe the dynamics. Suppose n = 2. Show that ...= 1 is an equilibrium. Sketch a graph and cobweb with c = 1/4. Does the equilibrium seem to be stable?
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1.11.14
Consider the following continuous system that approximates the
discontinuous model studied in this chapter ... for the
following values of n. Find the equilibria and their stability as a function of c, and describe the dynamics. Suppose n = 4. Show that ... = 1 is an equilibrium. Sketch a graph and cobweb with c = 1/4. Does the equilibrium seem to be stable?
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1.11.15 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Suppose h =1000 and ... =1000 and r = 1.5. Investigate some solutions starting with different values of ... < 1000. What is happening?
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1.11.16 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Find the equilibrium when h =1000 and ... =1000 and r = 1.5.
What would happen to solutions starting with values greater than the
equilibrium? Use this information, and that in the previous problem, to
sketch a cobweb diagram.
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1.11.17 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Redo Exercise 15 with r = 1.65. How do the results differ from those in Exercise 15?
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1.11.18 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Find the equilibrium when h =1000 and ... =1000 and r = 1.65. Can you explain why solutions that start below the equilibrium can shoot off to infinity?
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1.11.19 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Find the equilibrium when h =1000 and ... =1000 and r = 1.65.
Can you explain why solutions that start below the equilibrium can
shoot off to infinity? Study the dynamics of Exercises 1–4 for values
of c ranging
from 0.4 up to 1.0. Are there any cases where the behaviour is neither
2:1 AV block nor the Wenckebach phenomenon? How would you describe these
behaviors.
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1.11.20 Population
models with thresholds can also have unusual behavior. Evaluate the
following models where individuals emigrate when the population is
overly crowded. In particular, suppose h individuals leave if the population is larger than some critical value ... ... Find the equilibrium when h =1000 and ... =1000 and r = 1.65.
Can you explain why solutions that start below the equilibrium can
shoot off to infinity? What happens to the dynamics of the example
illustrated in Figure 1.11.10 if c is made even closer to 0.5? What does it look like on a cobwebbing diagram? If c = 0.5000000000001, do you think it would be possible to distinguish the Wenckebach phenomenon from normal beating? Is it?
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