 11.4.1: Suppose that the densities of two species evolve in accordance with...
 11.4.2: Suppose the densities of two species evolve in accordance with the ...
 11.4.3: In 36, use the graphical approach to classify the following LotkaVo...
 11.4.4: In 36, use the graphical approach to classify the following LotkaVo...
 11.4.5: In 36, use the graphical approach to classify the following LotkaVo...
 11.4.6: In 36, use the graphical approach to classify the following LotkaVo...
 11.4.7: In 710, use the eigenvalue approach to analyze all equilibria of th...
 11.4.8: In 710, use the eigenvalue approach to analyze all equilibria of th...
 11.4.9: In 710, use the eigenvalue approach to analyze all equilibria of th...
 11.4.10: In 710, use the eigenvalue approach to analyze all equilibria of th...
 11.4.11: Suppose that two species of beetles are reared together in one expe...
 11.4.12: Suppose that two species of beetles are reared together. Species 1 ...
 11.4.13: In 13 and 14, use a graphing calculator to sketch solution curves o...
 11.4.14: In 13 and 14, use a graphing calculator to sketch solution curves o...
 11.4.15: Assume that dN dt = N 4PN dP dt = 2PN 3P (a) Show that this system ...
 11.4.16: Assume that dN dt = 5N PN dP dt = PN P (a) Show that this system ha...
 11.4.17: Assume that N(t) denotes the density of an insect species at time t...
 11.4.18: Assume that N(t) denotes prey density at time t and P(t) denotes pr...
 11.4.19: An unrealistic feature of the LotkaVolterra model is that the prey ...
 11.4.20: An unrealistic feature of the LotkaVolterra model is that the prey ...
 11.4.21: An unrealistic feature of the LotkaVolterra model is that the prey ...
 11.4.22: (a) Find the zero isoclines of (11.90), and determine conditions un...
 11.4.23: Use the results of to show that an increase in a (the intrinsic rat...
 11.4.24: Use the results of to show that an increase in b (the searching eff...
 11.4.25: Use the results of to show that an increase in c (the predator grow...
 11.4.26: Use the results of to show that an increase in K (the prey carrying...
 11.4.27: In 2734, classify each community matrix at equilibrium according to...
 11.4.28: In 2734, classify each community matrix at equilibrium according to...
 11.4.29: In 2734, classify each community matrix at equilibrium according to...
 11.4.30: In 2734, classify each community matrix at equilibrium according to...
 11.4.31: In 2734, classify each community matrix at equilibrium according to...
 11.4.32: In 2734, classify each community matrix at equilibrium according to...
 11.4.33: In 2734, classify each community matrix at equilibrium according to...
 11.4.34: In 2734, classify each community matrix at equilibrium according to...
 11.4.35: In 3540, we consider communities composed of two species. The abund...
 11.4.36: In 3540, we consider communities composed of two species. The abund...
 11.4.37: In 3540, we consider communities composed of two species. The abund...
 11.4.38: In 3540, we consider communities composed of two species. The abund...
 11.4.39: In 3540, we consider communities composed of two species. The abund...
 11.4.40: In 3540, we consider communities composed of two species. The abund...
 11.4.41: Assume that the diagonal elements aii of the community matrix of a ...
 11.4.42: Consider a community composed of two species. Assume that both spec...
 11.4.43: The classical LotkaVolterra model of predation is given by dN dt = ...
 11.4.44: The modified LotkaVolterra model of predation is given by dN dt = a...
 11.4.45: Use a graphing calculator to study the following example of the Fit...
 11.4.46: Use a graphing calculator to study the following example of the Fit...
 11.4.47: Assume the following example of the FitzhughNagumo model: dV dt = V...
 11.4.48: Assume the following example of the FitzhughNagumo model: dV dt = V...
 11.4.49: In 4952, use the mass action law to translate each chemical reactio...
 11.4.50: In 4952, use the mass action law to translate each chemical reactio...
 11.4.51: In 4952, use the mass action law to translate each chemical reactio...
 11.4.52: In 4952, use the mass action law to translate each chemical reactio...
 11.4.53: Show that the following system of differential equations has a cons...
 11.4.54: Show that the following system of differential equations has a cons...
 11.4.55: Show that the following system of differential equations has a cons...
 11.4.56: Suppose that x(t) + y(t) is a conserved quantity. If dx dt = 3x + 2...
 11.4.57: The MichaelisMenten law [Equation (11.76)] states that dp dt = vms ...
 11.4.58: The growth of microbes in a chemostat was described by (11.77). Usi...
 11.4.59: The growth of microbes in a chemostat was described by (11.77). Usi...
 11.4.60: In 60 and 61, we investigate specific examples of microbial growth ...
 11.4.61: In 60 and 61, we investigate specific examples of microbial growth ...
Solutions for Chapter 11.4: Nonlinear Systems: Applications
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 11.4: Nonlinear Systems: Applications
Get Full SolutionsChapter 11.4: Nonlinear Systems: Applications includes 61 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688. This expansive textbook survival guide covers the following chapters and their solutions. Since 61 problems in chapter 11.4: Nonlinear Systems: Applications have been answered, more than 20184 students have viewed full stepbystep solutions from this chapter.

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Constant of variation
See Power function.

Continuous function
A function that is continuous on its entire domain

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Inductive step
See Mathematical induction.

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Linear system
A system of linear equations

Matrix element
Any of the real numbers in a matrix

Negative association
A relationship between two variables in which higher values of one variable are generally associated with lower values of the other variable.

nth root of unity
A complex number v such that vn = 1

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Radicand
See Radical.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Righthand limit of ƒ at x a
The limit of ƒ as x approaches a from the right.

Root of an equation
A solution.

Translation
See Horizontal translation, Vertical translation.