DYNAMICS AT INFINITY of A CUBIC CHUA'S SYSTEM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GLOBAL DYNAMICS of THE LORENZ SYSTEM WITH INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reaction dynamics under confinement: an exact path integral treatment of a two-stage model of stochastic gene expression

Gene expression in living systems is inherently stochastic, and tends to produce varying numbers of proteins over repeated cycles of transcription and translation. In this paper, an expression is derived for the steady-state protein number distribution starting from a two-stage kinetic model of the gene expression process involving p proteins and r mRNAs. The derivation is based on an exact path integral evaluation of the joint distribution, P(p, r, t), of p and r at time t, which can be expressed in terms of the coupled Langevin equations for p and r that represent the two-stage model in continuum form. The steady-state distribution of p alone, P(p), is obtained from P(p, r, t) (a bivariate Gaussian) by integrating out the r degrees of freedom and taking the limit t -> infinity. P(p) is found to be proportional to the product of a Gaussian and a complementary error function. It provides a generally satisfactory fit to simulation data on the same two-stage process when the translational efficiency (a measure of intrinsic noise levels in the system) is relatively low; it is less successful as a model of the data when the translational efficiency (and noise levels) are high.

Transition from dissipative to conservative dynamics in equations of hydrodynamics

We show, by using direct numerical simulations and theory, how, by increasing the order of dissipativity (alpha) in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case alpha -> infinity U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of alpha greater than a crossover value alpha(crossover). We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows.

Descending from infinity: Convergence of tailed distributions

We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not eliminated. Relaxation stronger than linear suppresses long tails immediately, but may lead to strong transient peaks in the probability distribution. We also find that a delta-function initial distribution under stronger than linear decay displays not one but two different regimes of diffusive spreading.

Collective dynamics of glass-forming polymers at intermediate length scales: a synergetic combination of neutron scattering, atomistic simulations and theoretical modelling

Qens/wins 2014 - 11th International Conference on Quasielastic Neutron Scattering and 6th International Workshop on Inelastic Neutron Spectrometers / editado por:Frick, B; Koza, MM; Boehm, M; Mutka, H

Population dynamics and stock assessment of Koth (Otolithoides biauritus Cantor, 1850) along the north-west coast of India

MSY, growth, selection and mortality parameters of Otolithoides biauritus have been worked out from data collected by MFV Saraswati of CIFE, and length frequency data from Ferry Wharf, Sasson dock, and Versova fish landing centres of Bombay. Values of L infinity, K, and t omicron obtained from length frequency study are 1572 mm, 0.2633/yr and 0.0289 yr respectively, and of weight growth parameters are W infinity = 10067 g, K = 0.03904/yr and t omicron = 0.0137 yr. Selection parameters are L + 150 mm, t sub(r) + 0.4167 yr lc + 240 mm and t omicron = 0.6367 yr. Selection factor (K) for codent worked out to be 12. Based on Z = 0.6486, the MSY of O. biauritus off northwest coast of India is assessed as 1,802 tons which is slightly higher than the current catch level of 1,634 tons.

Biological characteristics and determination of population dynamics parameters of Nemipterus japonicus in the coastal waters of Province Bushehr, Persian Gulf

This study was conducted to determine biological characteristics and population dynamics parameters of threadfin bream (Nemipterus japonicus) in Persian Gulf (Bushehr Province), during November 2006 and October 2007. The minimum and maximum specimens were 75-273 mm FL and their weight was 7.6 - 351.9 g. Based on the exponential relationship between fork length and weight, slope (b) for individuals, males and females was 2.987321, 2.992546 and 3.007314, respectively. The emptiness value (V) was 45.6% and it shows that N. japonicus is a moderate feeder. The results of Fp indicates that crustacean with 78.2% are main foods, mollusca (27.7%), fishes (20.7%), polychaeta (19.2%) and Foraminifera (11.7%) were identified as minor foods and phytoplanktons (9.9%), nematoda(8.0%), echinodermata (2.3%) and sea weeds (0.3%) were random foods. The reproduction studies showed the spawning season extended within 2 peaks, from April- May and September and main spawning occurs in spring season.The mean absolute and relative fecundities were 472388±42633 and 3817±293 (X±SE), respectively. The maximum, minimum and mean of oocyte diameter were 0.448, 0.022 and 0.221mm (SE=0.071), respectively.The fork length at 50% maturity estimated to be 20.25 cm for females. The growth coefficient (K) , length infinity (L∞ ) and ɸ' was estimated 0.42/yr , 34.17 cm and 2.69, respectively. The coefficient of total mortality, fishing mortality, natural mortality and E was 1.37, 0.43, 0.94 and 0.31, respectively.

Population dynamics and stock assessment of the common carp (Cyprinus carpio) in Iranian waters of the Caspian Sea

In order to come up with the responsible fishing pattern of common carp, there was a need to identify some of the biological characteristics and stock assessment of carp in Iranian waters of the Caspian Sea .The fork length ,weight ,age ,growth parameters of von bertalanffy and mortality rates of common carp were estimated from oct 2006 to sept 2007.Based on the exponential relationship between length and weight in the size range 6.3-65.6 cm ,b was calculated 2.895, 2.843 and 2.925 respectively for combined sexes ,males and females. The mean condition factor was 1.9 which is close to the ideal condition.The results from measuring 3170 specimens ,were showed the first fork length of maturity was 30 cm for males and 32 cm for females. The results indicated that females were predominate and sex ratio was 0.66:1 (M:F) and chi-squares analysis showeda significant difference between males and females.(p<0.05).Length infinity and growth coefficient were calculated by three different methods as below: Length frequency analysis : k=0.17 L∞ =68.04 Age-Length Key k=0.15 L∞ =74.25 Back calculation : k=0.14 L∞ =68.4 The mortality parameters and exploitation rate were estimated as below : Z=0.73 per year M=0.31 per year F=0.42 per year E=0.56 Refer to amount of common carp catch in 2007 -08 ,biomass was calculated 9640.2 tones by jone's cohort analysis and MSY 2374.5 tones.According to analysis ,the number of common carp in the distribution area (Iranian part of the Caspian Sea ) was estimated 24 millions in the 2006-07.

Population dynamics and management of yellowfin tuna (Thunnus albacares) of the Oman Sea

The Yellowfin tuna was caught more than all other species in the southern waters of Iran (24000 tons in 1998). In order to come up with the responsible fishing pattern, there was a need to identify some of the biological characteristics and population dynamic parameters. This thesis was the first which covered the whole Yellowfin tuna distribution in the Oman Sea, included the fishing grounds of Berris, Ramin, Chabahar, Pozm and Jask. The data during 1998-99 from different fishing grounds were polled. Based on the exponential relationship between length and weight in the size range 38-173 Cm, the relationship (W=aL^ b) was calculated as W=0.000012L ^ 3.0831). The mean fork length,head length,girth and weight were calculated respectively 84.15 Cm, 23 Cm, 53 Cm, and 11828 g. Length infinity was estimated 189 Cm with growth parameters of 0.42 per year. Growth performance index was 4.18 which was in agreement with the findngs of the other studies in the Indian and Pacific Oceans. The mortality parameters and exploitation rate were estimated as below: Z = 1.75-1.85 M=0.6 F=1.25 E=0.68 Occurence of empty stomach was high (60%) in the speciemens obtained from the Oman Sea. Purpleback flying squid (Sthenoteuthis oualaniensis) was the most dominant prey species observed in the study (57% in females and 60% in males), occurrence of teleost fishes were found to be the second (38% in males and 42% in females). Crabs also were identified in the specimens(1-2%). The study on sex ratio indicated that males were predominant at all sizes above 120 Cm fork length. 50.82% of specimens were males and 49.18% females. The monthly gonadosomatic index was deriven higher values during January to June which could be indicated as spawning period.

Dynamics of the viscous Cahn-Hilliard equation

We study generalized viscous Cahn-Hilliard problems with nonlinearities satisfying critical growth conditions in W-0(1,p)(Omega), where Omega is a bounded smooth domain in R-n, n >= 3. In the critical growth case, we prove that the problems are locally well posed and obtain a bootstrapping procedure showing that the solutions are classical. For p = 2 and almost critical dissipative nonlinearities we prove global well posedness, existence of global attractors in H-0(1)(Omega) and, uniformly with respect to the viscosity parameter, L-infinity(Omega) bounds for the attractors. Finally, we obtain a result on continuity of regular attractors which shows that, if n = 3, 4, the attractor of the Cahn-Hilliard problem coincides (in a sense to be specified) with the attractor for the corresponding semilinear heat equation. (C) 2008 Elsevier Inc. All rights reserved.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)