By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length ξδ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant g and for certain lattice maps, the Lyapunov dimension density and other dynamic...

We prove that every chain of odd power integrators perturbed by a C triangular vector eld can be stabilized in the large via continuous state feedback, although it is not stabilizable, even locally, by any smooth state feedback. The proof is constructive and accomplished by developing a machinery|a continuous type of adding a power integrator|that enables one to explicitly design a C globally s...

In this paper, we would like to disseminate a serendipitous discovery involving Lyapunov exponents of a 1-D time series and their use in serving as a filtering defense tool against a specific kind of deep adversarial perturbation. To this end, we use the state-of-the-art CleverHans library to generate adversarial perturbations against a standard Convolutional Neural Network (CNN) architecture t...

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...

The application of optimization techniques derived from the study of Euclidean full Steiner Trees to macromolecules like proteins is reported in the present work. We shall use the concept of Euclidean Steiner Ratio Function (SRF) as a good Lyapunov function in order to perform an elementary stability analysis.

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...

In this paper, we introduce Lyapunov measure to verify weak (a.e.) notions of stability for an invariant set of a nonlinear dynamical system. Using certain linear operators from Ergodic theory, we derive Lyapunov results to deduce a.e. stability. In order to highlight the linearity of our approach, we also provide explicit formulas for obtaining Lyapunov function and Lyapunov measure in terms o...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

In planar analytic vector fields, a monodromic singularity can be distinguished between focus or center by means of the Lyapunov coefficients, which are given in terms power series coefficients first-return map defined around singularity. this paper, we interested an analogous problem for tangential singularities piecewise fields $Z=(Z^+ ,Z^-)$. First, prove that map, neighborhood singularity, ...