I have a question which asks: At what value of b does the quadratic 1.5x^2+bx+2.34 move from having a stable fixed point to having a stable period 2 point? How would I go about solving this?
2026-03-25 22:04:09.1774476249
Value of b which moves quadratic from a stable fixed point to a stable period 2 point
100 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in NUMERICAL-METHODS
- The Runge-Kutta method for a system of equations
- How to solve the exponential equation $e^{a+bx}+e^{c+dx}=1$?
- Is the calculated solution, if it exists, unique?
- Modified conjugate gradient method to minimise quadratic functional restricted to positive solutions
- Minimum of the 2-norm
- Is method of exhaustion the same as numerical integration?
- Prove that Newton's Method is invariant under invertible linear transformations
- Initial Value Problem into Euler and Runge-Kutta scheme
- What are the possible ways to write an equation in $x=\phi(x)$ form for Iteration method?
- Numerical solution for a two dimensional third order nonlinear differential equation
Related Questions in BIFURCATION
- Looking for references about a graphical representation of the set of roots of polynomials depending on a parameter
- What type of bifurcation point is this?
- Dynamical Systems - Find bifurcation point, draw bifurcation diagram and classify bifurcations
- Codimension 3+ bifurcations?
- Find Polar Differential Equation that satisfies Bifurcation Diagram
- Bifurcation point of $\theta' =\frac{\sin \theta}{r+\sin\theta}$
- Can a hyperbolic fixed point be inside a homoclinic loop on a plane?
- What does it mean to find a normal form of a saddle node bifurcation?
- Reference and applications of Bifurcation theory
- Is bifurcation analysis automatized?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It sounds like you are iterating $x_{i+1}=1.5x_i^2+bx_i+2.34$ You can find the fixed point by solving $x_{i+1}=x_i$, giving the quadratic $x=1.5x^2+bx+2.34$. The fixed point will be a function of $b$. It is stable if the derivative of $1.5x^2+bx+2.34$ evaluated at the fixed point has absolute value less than $1$. This is because the slope of the curve is the factor the error is multiplied by each step. If the absolute value is less than 1, you get closer. If the absolute value is greater than 1, you get farther away.