arXiv subjects
Publications and source records attributed to Ricardo Lopez-Ruiz.
Lienard systems of the form $\ddot{x}+εf(x)\dot{x}+x=0$, with f(x) an even function, are studied in the strongly nonlinear regime ($ε\to\infty$). A method for obtaining the number, amplitude and loci of the limit cycles of these equations is derived. The accuracy of this method is checked in several examples. Lins-Melo-Pugh conjecture for the polynomial case is true in this regime.
Lienard systems of the form $\ddot{x}+εf(x)\dot{x}+x=0$, with f(x) an even continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak ($ε\to 0$) and in the strongly ($ε\to\infty$) nonlinear regime in some examples. The number of limit cycles does not increase when $ε$ increases from zero to infinity in all the cases analyzed.
The LMC-complexity introduced by Lopez-Ruiz, Mancini and Calbet [Phys. Lett. A 209, 321-326 (1995)] is calculated for different physical situations: one instance of classical statistical mechanics, normal and exponential distributions, and a simplified laser model. We stand out the specific value of the population inversion for which the laser presents maximun complexity.
The time evolution equations of a simplified isolated ideal gas, the "tetrahe- dral" gas, are derived. The dynamical behavior of the LMC complexity [R. Lopez-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in this system. In general, it is shown that the complexity remains within the bounds of minimum and maximum complexity. We find that there are certain restrictions when the isolated "tetrahedral" gas evolves towards equilibrium. In addition to the well-known increase in entropy, the quantity called disequilibrium decreases monotonically with time. Furthermore, the trajectories of the system in phase space approach the maximum complexity.
Basins generated by a noninvertible mapping formed by two symmetrically coupled logistic maps are studied when the only parameter λof the system is modified. Complex patterns on the plane are visualised as a consequence of basins' bifurcations. According to the already established nomenclature in the literature, we present the relevant phenomenology organised in different scenarios: fractal islands disaggregation, finite disaggregation, infinitely disconnected basin, infinitely many converging sequences of lakes, countable self-similar disaggregation and sharp fractal boundary. By use of critical curves, we determine the influence of zones with different number of first rank preimages in the mechanisms of basin fractalization.
We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some choice. In the present study, several possibilities appear available. One of them is examined in detail. Some interesting properties desirable for any magnitude of complexity are discovered on this particular extension.
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of radial and angular oscillations, that holds for both small and high energy trajectories, is obtained. This relation allows us to identify the closed orbits of the system. The virtues of this model to illustrate pedagogically, how in a physical system, the energy is transferred between different modes, are also emphasized. Two easy identification criteria for this type of motion with potential interest in industrial design are obtained.