I'm treating with a nonlinear bidimensional system of ODE, in which one of my fixed points is non-hyperbolic, that is, its eigenvalues has ($\Re(\lambda_{1,2}) = 0$). Therefore, I cannot say anything about its stability from the linear analysis once it does not satisfy Hartman-Grobman theorem. To overcome this difficulty I want to use Floquet's method to define the stability of the closed orbit, but apparently this should be used for linear systems. My doubt is: Can I use Floquet's method in the linerized system? If not, is there any nonlinear kind of Floquet's treatment?
2026-03-25 01:29:23.1774402163
Usage of Floquet's Method
115 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ORDINARY-DIFFERENTIAL-EQUATIONS
- The Runge-Kutta method for a system of equations
- Analytical solution of a nonlinear ordinary differential equation
- Stability of system of ordinary nonlinear differential equations
- Maximal interval of existence of the IVP
- Power series solution of $y''+e^xy' - y=0$
- Change of variables in a differential equation
- Dimension of solution space of homogeneous differential equation, proof
- Solve the initial value problem $x^2y'+y(x-y)=0$
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Derive an equation with Faraday's law
Related Questions in DYNAMICAL-SYSTEMS
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- Determine $ \ a_{\max} \ $ and $ \ a_{\min} \ $ so that the above difference equation is well-defined.
- Question on designing a state observer for discrete time system
- How to analyze a dynamical system when $t\to\infty?$
- The system $x' = h(y), \space y' = ay + g(x)$ has no periodic solutions
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
- Including a time delay term for a differential equation
- Doubts in proof of topologically transitive + dense periodic points = Devaney Chaotic
- Condition for symmetric part of $A$ for $\|x(t)\|$ monotonically decreasing ($\dot{x} = Ax(t)$)
Related Questions in STABILITY-IN-ODES
- Stability of system of ordinary nonlinear differential equations
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- How to analyze a dynamical system when $t\to\infty?$
- The system $x' = h(y), \space y' = ay + g(x)$ has no periodic solutions
- Existence of unique limit cycle for $r'=r(μ-r^2), \space θ' = ρ(r^2)$
- Intuitive proof of Lyapunov's theorem
- Stability of a nonlinear ODE system (only existence of the limit)
- Deriving inequality from a Lyapunov test of $x' = -x + y^3, \space y' = -y + ax^3$
- does the order lineariztion/evaluation matter here?
Related Questions in STABILITY-THEORY
- MIT rule VS Lyapunov design - Adaptive Control
- Stability of system of parameters $\kappa, \lambda$ when there is a zero eigenvalue
- Stability of stationary point $O(0,0)$ when eigenvalues are zero
- How to analyze a dynamical system when $t\to\infty?$
- Intuitive proof of Lyapunov's theorem
- Deriving inequality from a Lyapunov test of $x' = -x + y^3, \space y' = -y + ax^3$
- Existence and uniqueness of limit cycle for $r' = μr(1-g(r^2)), \text{and} θ' = p(r^2)$
- Omega limit set $\omega(x_0)$ for $r' = 2μr(5-r^2), \space θ' = -1$
- Show that $x_1' = x_2, \space x_2' = -2x_1 + x_2(2-5x_1^2 - 3x_2^2)$ has a bounded solution
- Region of attraction and stability via Liapunov's function
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?