- 11.5.1: x' = 2 + xy y' = x -y
- 11.5.2: x' = 2x -xy y' = -1 - x2 + 2x -y2
- 11.5.3: x' = -x + y2 y' = x -y
- 11.5.4: x' = xy2 - x2y y' = x2y -1
- 11.5.5: x' = -x- y y' = x + y3 for< 0
- 11.5.6: x' = 2x + y2 y' = xy-y
- 11.5.7: x' -2x + (x')4 = 0
- 11.5.8: x' + x = [! + 3(x')2]x' - i2
- 11.5.9: x' = -2x + xy y' = 2y - i
- 11.5.10: x' = -x3 + 4x y' = -5i2 -y2
- 11.5.11: Show that the plane autonomous system x' = x(l - i2 -3y2) y' = y(3 ...
- 11.5.12: If ag/ax' i= 0 in a region R, prove that x" = g(x, x') has no perio...
- 11.5.13: Show that the predator-prey model x' -ax+ bxy r y' = -cxy + -y(K -y...
- 11.5.14: x' = -y -xe'+y y' = x -ye'+y
- 11.5.15: x' = -x + y + xy y' = x -y - i2 -y3
- 11.5.16: Verify that the region bounded by the closed curve YI> + 3y2 = 1 is...
- 11.5.17: The plane autonomous system in Example 8 has only one critical poin...
- 11.5.18: Use the Poincare-Bendixson theorem to show that the secondorder non...
- 11.5.19: Let X = X(t) be the solution of the plane autonomous system x' = Y ...
- 11.5.20: Investigate global stability for the system x' = y-x y' = -x -y3
- 11.5.21: Empirical evidence suggests that the plane autonomous system x' = i...
- 11.5.22: (a) Find and classify all critical points of the plane autonomous s...
Solutions for Chapter 11.5: Periodic Solutions, Limit Cycles, and Global Stability
Full solutions for Advanced Engineering Mathematics | 5th Edition
Solutions for Chapter 11.5: Periodic Solutions, Limit Cycles, and Global StabilityGet Full Solutions
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.
A method of variable selection in regression that begins with all of the candidate regressor variables in the model and eliminates the insigniicant regressors one at a time until only signiicant regressors remain
An experiment in which the treatments (experimental conditions) that are to be studied are included in the experiment. The data from the experiment are used to evaluate the treatments.
Components of variance
The individual components of the total variance that are attributable to speciic sources. This usually refers to the individual variance components arising from a random or mixed model analysis of variance.
Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.
The variance of the conditional probability distribution of a random variable.
The probability 1?a associated with a conidence interval expressing the probability that the stated interval will contain the true parameter value.
A correction factor used to improve the approximation to binomial probabilities from a normal distribution.
A two-dimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .
Used in statistical quality control, a defect is a particular type of nonconformance to speciications or requirements. Sometimes defects are classiied into types, such as appearance defects and functional defects.
Defect concentration diagram
A quality tool that graphically shows the location of defects on a part or in a process.
W. Edwards Deming (1900–1993) was a leader in the use of statistical quality control.
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.
Estimate (or point estimate)
The numerical value of a point estimator.
Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.
Goodness of fit
In general, the agreement of a set of observed values and a set of theoretical values that depend on some hypothesis. The term is often used in itting a theoretical distribution to a set of observations.