Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.

A wide-spread belief that nested bars enhance gas inflow to the galactic centre has recently been contradicted by dynamical models in which inner bars seem to prohibit such inflow. Can the existing models of dynamically possible double bars be modified to enable strong inflow in the secondary bar? I present here simple dynamical arguments which imply that in general, double bars in resonant cou...

We study a Crank–Nicolson type time discretisation (known as Tustin’s method in engineering literature) for a conservative, infinite-dimensional linear dynamical system whose transfer function is scalar and inner. We show that this discretisation approximates the state trajectory at any given time. We first prove the result for canonical Hankel range realisations, and the general case is then o...

In this paper, global uniform exponential stability of perturbed dynamical systems is studied by using Lyapunov techniques. The system presents a perturbation term which is bounded by an integrable function with the assumption that the nominal system is globally uniformly exponentially stable. Some examples in dimensional two are given to illustrate the applicability of the main results.

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters D & 10 km in the current asteroid belt. In a numerical analysis of the long term evolution of test particles in the main asteroid belt region, we find that the dynamical loss h...

Inverse iteration is a standard technique for nding selected eigenvectors associated with eigenvalues which are known approximately. At each step the solution of a linear system of equations is required, which is usually done by factorizing the system matrix. When direct factorization is impractical, iterative methods can be applied for solving the linear systems. Several results about terminat...

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...

4D variational data assimilation is proposed as an efficient procedure to determine a past configuration of a dynamical system of which only a few (and, under certain hypothesis, even partial) observations and its dynamics are known. The retrieved configuration is in good accordance with the test configuration. The leading mathematical concept, adjoint equations, and the role in the design of a...

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...