Planar nonautonomous polynomial equations: The Riccati equation

Planar Nonautonomous Polynomial Equations Iv . Nonholomorphic Case

We give a few sufficient conditions for the existence of periodic solutions of the equation ż = Pn j=0 aj(t)z j − Pr k=1 ck(t)z k where n > r and aj ’s, ck’s are complex valued. We prove the existence of one up to two periodic solutions.

Chaos in some planar nonautonomous polynomial differential equation

We show that under some assumptions on the function f the system ż = z(f(z)e + ei2φt) generates chaotic dynamics for sufficiently small parameter φ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

Existence conditions for stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation

In this paper several necessary and sufficient conditions for existence of stabilizing and antistabilizing solutions to the nonautonomous matrix Riccati differential equation (RDE) are presented. The conditions are reduced to existence of a solution to the corresponding Riccati type matrix inequality, or to existence of exponential dichotomy for the associated Hamiltonian linear differential sy...

Fractional Riccati Equation Rational Expansion Method For Fractional Differential Equations

In this paper, a new fractional Riccati equation rational expansion method is proposed to establish new exact solutions for fractional differential equations. For illustrating the validity of this method, we apply it to the nonlinear fractional Sharma-TassoOlever (STO) equation, the nonlinear time fractional biological population model and the nonlinear fractional foam drainage equation. Compar...

Improving the Accuracy of the Solutions of Riccati Equations