Invariants of kinetic differential equations.
On the generalized Floquet theory of disconjugate 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...
Oscillatory Solutions in the Planar Restricted Three-Body Problem.
Periodic points and chaotic-like dynamics of planar maps associated to nonlinear Hill's equations with indefinite weight.
Phase synchronization in coupled Sprott chaotic systems presented by fractional differential equations.
Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations
We study the vibration of lumped parameter systems whose constituents are described through novel constitutive relations, namely implicit relations between the forces acting on the system and appropriate kinematical variables such as the displacement and velocity of the constituent. In the classical approach constitutive expressions are provided for the force in terms of appropriate kinematical variables, which when substituted into the balance of linear momentum leads to a single governing ordinary...
Some problems concerning different types of vector valued almost periodic functions [Book]
Stability of a two-strain tuberculosis model with general contact rate.
Statistical mechanics of nonlinear wave equations
Switched modified function projective synchronization between two complex nonlinear hyperchaotic systems based on adaptive control and parameter identification
This paper investigates adaptive switched modified function projective synchronization between two complex nonlinear hyperchaotic systems with unknown parameters. Based on adaptive control and parameter identification, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve switched modified function projective synchronization between two different complex nonlinear hyperchaotic systems and to estimate the unknown system parameters. A numerical simulation...
Synthesis of chaotic systems
Tangencies for real and complex Hénon maps: An analytic method.
Tauberian theorems for vector-valued Fourier and Laplace transforms
Let X be a Banach space and be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
Topological entropy and differential equations
On the background of a brief survey panorama of results on the topic in the title, one new theorem is presented concerning a positive topological entropy (i.e. topological chaos) for the impulsive differential equations on the Cartesian product of compact intervals, which is positively invariant under the composition of the associated Poincaré translation operator with a multivalued upper semicontinuous impulsive mapping.
Trajectory sensitivity method and master-slave synchronization to estimate parameters of nonlinear systems.
Trichotomy and bounded solutions of nonlinear differential equations
The existence of bounded solutions for equations in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation satisfies some conditions expressed in terms of measures of noncompactness.
Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium