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  2. Hopf bifurcation - Wikipedia

    en.wikipedia.org/wiki/Hopf_bifurcation

    Complex eigenvalues of an arbitrary map (dots). In case of the Hopf bifurcation, two complex conjugate eigenvalues cross the imaginary axis. In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic solution arises. [1]

  3. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The solution set for the equations xy = −1 and 3x + y = 9 is the single point (2, 3). A solution of a linear system is an assignment of values to the variables ,, …, such that each of the equations is satisfied. The set of all possible solutions is called the solution set. [5]

  4. Consistent and inconsistent equations - Wikipedia

    en.wikipedia.org/wiki/Consistent_and...

    The system + =, + = has exactly one solution: x = 1, y = 2 The nonlinear system + =, + = has the two solutions (x, y) = (1, 0) and (x, y) = (0, 1), while + + =, + + =, + + = has an infinite number of solutions because the third equation is the first equation plus twice the second one and hence contains no independent information; thus any value of z can be chosen and values of x and y can be ...

  5. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    This is the case, for example, if f(x) = x 3 − 2x + 2. For this function, it is even the case that Newton's iteration as initialized sufficiently close to 0 or 1 will asymptotically oscillate between these values. For example, Newton's method as initialized at 0.99 yields iterates 0.99, −0.06317, 1.00628, 0.03651, 1.00196, 0.01162, 1.00020 ...

  6. Today’s NYT ‘Strands’ Hints, Spangram and Answers for ...

    www.aol.com/today-nyt-strands-hints-spangram...

    For every 3 non-theme words you find, you earn a hint. Hints show the letters of a theme word. If there is already an active hint on the board, a hint will show that word’s letter order.

  7. NYT ‘Connections’ Hints and Answers Today, Wednesday, December 11

    www.aol.com/nyt-connections-hints-answers-today...

    today's connections game answers for wednesday, december 11, 2024: 1. utopia: paradise, seventh heaven, shangri-la, xanadu 2. things you shake: hairspray, magic 8 ...

  8. Puzzle solutions for Sunday, Dec. 1, 2024

    www.aol.com/news/puzzle-solutions-sunday-dec-1...

    7 Little Words. ICELAND. BULGARIA. GREECE. NETHERLANDS. AUSTRIA. MOLDOVA. SWITZERLAND (Distributed by Andrews McMeel) Find the Words. Meal preparation station (Distributed by Creators Syndicate) Kubok

  9. Basic feasible solution - Wikipedia

    en.wikipedia.org/wiki/Basic_feasible_solution

    Here, m=2 and there are 10 subsets of 2 indices, however, not all of them are bases: the set {3,5} is not a basis since columns 3 and 5 are linearly dependent. The set B={2,4} is a basis, since the matrix = is non-singular.