On -stability of nonlinear Lyapunov matrix differential equations.
Optimal, adaptive and single state feedback control for a 3D chaotic system with golden proportion equilibria
In this paper, the problems on purposefully controlling chaos for a three-dimensional quadratic continuous autonomous chaotic system, namely the chaotic Pehlivan-Uyaroglu system are investigated. The chaotic system, has three equilibrium points and more interestingly the equilibrium points have golden proportion values, which can generate single folded attractor. We developed an optimal control design, in order to stabilize the unstable equilibrium points of this system. Furthermore, we propose...
Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity
Periodic parametric perturbation control and dynamics at infinity for a 3D autonomous quadratic chaotic system are studied in this paper. Using the Melnikov's method, the existence of homoclinic orbits, oscillating periodic orbits and rotating periodic orbits are discussed after transferring the 3D autonomous chaotic system to a slowly varying oscillator. Moreover, the parameter bifurcation conditions of these orbits are obtained. In order to study the global structure, the dynamics at infinity...
Periodic solutions of the third order parametric differential equations involving large nonlinearities
Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces
We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness...
Periodicity and stability results for solutions of some fifth order nonlinear differential equations
Perron conditions and uniform exponential stability of linear skew-product semiflows on locally compact spaces.
Phasenraum-Methoden zum Studium nichtlinearer Differentialgleichungen.
Practical Lyapunov stability criteria for differential algebraic equations
Practical Stability in Terms of Two Measures for Hybrid Dynamic Systems
We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.
Problème général de la stabilité du mouvement
Qualitative analysis for a class of plane systems.
Razumikhin's method in the qualitative theory of processes with delay.
Remarks on stability of inverted pendula.
Remarque sur la méthode de la variation de la constante généralisée
Repelling conditions for boundary sets using Liapunov-like functions. I. - Flow-invariance, terminal value problem and weak persistence
Resolvents, integral equations, limit sets
In this paper we study a linear integral equation , its resolvent equation , the variation of parameters formula , and a perturbed equation. The kernel, , satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.
Restricted total stability and total attractivity.
Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point
Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations.