WebMar 11, 2024 · The 4 differential equations above are added into a Mathematica code as “eqns” and “s1” is the fixed points of the differentials. The steady state values found for “a, b, c, and d” are called "s1doubleBrackets(7)” After the steady state values are found, the Jacobian matrix can be found at those values. WebFixed point theory is one of the outstanding fields of fractional differential equations; see [22,23,24,25,26] and references therein for more information. Baitiche, Derbazi, Benchohra, and Cabada [ 23 ] constructed a class of nonlinear differential equations using the ψ -Caputo fractional derivative in Banach spaces with Dirichlet boundary ...
Fixed Point -- from Wolfram MathWorld
WebFixed point theory is one of the outstanding fields of fractional differential equations; see [22,23,24,25,26] and references therein for more information. Baitiche, Derbazi, Benchohra, and Cabada [ 23 ] constructed a class of nonlinear differential equations using the ψ -Caputo fractional derivative in Banach spaces with Dirichlet boundary ... WebFrom the equation y ′ = 4 y 2 ( 4 − y 2), the fixed points are 0, − 2, and 2. The first one is inconclusive, it could be stable or unstable depending on where you start your trajectory. − 2 is unstable and 2 is stable. Now, there are two ways to investigate the stability. or47-sd2s-80-2
Nonlinear ode: fixed points and linear stability - YouTube
WebApr 14, 2024 · In the current paper, we demonstrate a new approach for an stabilization criteria for n-order functional-differential equation with distributed feedback control in the integral form. We present a correlation between the order of the functional-differential equation and degree of freedom of the distributed control function. We present two … WebThis paper is devoted to studying the existence and uniqueness of a system of coupled fractional differential equations involving a Riemann–Liouville derivative in the Cartesian product of fractional Sobolev spaces E=Wa+γ1,1(a,b)×Wa+γ2,1(a,b). Our strategy is to endow the space E with a vector-valued norm and apply the Perov fixed point theorem. WebJan 2, 2024 · Dividing the second equation by the first equation in (6.16) gives: ˙y ˙x = dy dx = − y x + x. This is a linear nonautonomous equation. A solution of this equation passing through the origin is given by: y = x2 3, It is also tangent to the unstable subspace at the origin. It is the global unstable manifold. We examine this statement further. or4-dell-5090-h-w10