We study the existence or nonexistence of true trajectories of chaotic dynamical systems that lie close to computer-generated trajectories. The nonexistence of such shadowing trajectories is caused by finite-time Lyapunov exponents of the system fluctuating about zero. A dynamical mechanism of the unshadowability is explained through a theoretical model and identified in simulations of a typica...

The paper investigates the dynamic modes of Sel’kov fractional self-oscillating system in order to simulate interaction cracks. spectra maximum Lyapunov exponents, constructed depending on parameters system, are used as a research tool. exponents were according Benettin-Wolf algorithm. It is shown that existence chaotic regimes possible. In particular, spectrum derivative contains positive valu...

We study the A-hypergeometric system associated with a monomial curve XA. We explicitly construct all rational solutions and show that XA is arithmetically Cohen-Macaulay if for all values of the exponents, the holonomic rank of the system equals the degree d of the curve. In the case of integral exponents we construct d independent solutions in terms of the roots of the generic univariate poly...

In this paper, we consider discrete and continuous QR algorithms for computing all of the Lyapunov exponents of a regular dynamical system. We begin by reviewing theoretical results for regular systems and present general perturbation results for Lyapunov exponents. We then present the algorithms, give an error analysis of them, and describe their implementation. Finally, we give several numeri...

In this paper we describe the maximal and the minimal values of Lyapunov exponents for second order discrete time invariant linear system perturbed by time varying bounded perturbation. The results may be interpreted in terms of generalized spectral radius and applied to obtained formulas for robust stability problem. Key-Words: Time varying discrete linear systems, Lyapunov exponents, robust s...

Table 2: Confusion matrix with 93.30% rec. rate and 1.39% error rate. 9 Acknowledgments The authors thanks ELSAG S.p.A., Italy, for supplying the character database and all researchers and staa of IRST that have contributed to this work. 15 Figure 5: A random subsample of size normalized characters. Second, values of free parameters are learned through a gradient-descent based algorithm. The cl...