Chaotic Transition Research Articles

Stability analysis of two coupled Lorenz lasers and the coupling-induced periodic →chaotic transition

We have performed a linear stability analysis of two Lorenz lasers coupled by their electric fields and have shown that the bad cavity condition becomes a function of coupling and that a good cavity instability may occur if the injected fields are inverted before injection. In addition, we show that the symmetrically coupled Lorenz system is isomorphic to the original Lorenz system with new parameters. The stability analysis also predicts a lowering of the second laser threshold with coupling for both the chaotic and self-pulsing regimes. Numerical integration of the equations is in agreement with these predictions and has revealed a coupling induced transition from self-pulsing to chaotic behavior. The classification of the behavior of the coupled system in the parameter space of the coupling constants has been investigated and shows that the results of symmetric coupling allow enough of a margin for an experimental test of the theory. This would allow experimentalists to observe the actual Lorenz instability at excitations as low as 4–5 times above threshold.

Chaos in the long-term behavior of some Bianchi-type VIII models

The long-term behavior of Bianchi-type VIII models with three different types of stress-energy tensors are examined and compared. The vacuum model, a matter-filled model, and a model with an electromagnetic field are considered. In each case the existence of chaotic behavior and transitions to chaotic behavior are discussed.

Nonadiabatic interactions of anharmonically coupled oscillators

The validity of the adiabatic approximation applied to systems of two coupled oscillators–typically represented by the Henon–Heiles’ Hamiltonian–is examined. Through explicit analytical estimates of nonadiabatic couplings, it is shown that the adiabatic approximation is appropriate in all cases, except for the case of 1:1 Fermi resonance between the two oscillators. In this case, nonadiabatic couplings are found to be important already at an excitation energy of about two quanta, i.e., at much lower energies than Ec, the critical energy for the classically observed quasiperiodic–chaotic transition. Nonadiabatic interactions are dominantly horizontal at these energies (E<Ec), however, indicating some regularity in the energy spectrum at low excitation, despite the early breakdown of the adiabatic separation.

Improved characteristics of Nb3Ge tunnel junctions using sputter-deposited amorphous-silicon barrier

We have fabricated Nb3Ge/amorphous-silicon/Pb Josephson tunnel junctions using high Tc(≥20 K) and stoichiometric (25±1 at. %Ge) Nb3Ge films. Good I-V characteristic with large Josephson current Ic and high gap voltage is obtained when the amorphous-silicon barrier is sputter deposited at low rf voltage and high Ar pressure to reduce the damage to the Nb3Ge by the sputtered particles and to obtain good coverage over the Nb3Ge surface. Peculiar I-V characteristics showing the inverse ac Josephson effect and chaotic transition betwen current steps are observed in the response to microwave. The temperature dependence of Ic agrees well with the theoretical calculation when the Ge enrichment at the top surface of the Nb3Ge electrode is reduced.

Scaling Behaviors of Characteristic Exponents near Chaotic Transition Points

On etudie le systeme X t+1 =X t +p r (X t ), (p r (X+1)=p r (X)) pres de ses points de transition de diffusion induite par chaos. On decouvre les proprietes d'echelle des exposants caracteristiques

U-Sequences in the Periodically Forced Brusselator

We show numerical evidence of exact U-sequences in the periodically forced trimolecular model (the forced Brusselator). Interspersed among period-doubling bifurcation sequences star-ting with RLn type periods, there are chaotic regions bounded on one side by period-doubling bifurcation sequences and on the other side by intermittent transitions. Along certain directions in the parameter space the most clearly seen periods appear in the same order as that in the logistic map, but along other directions the U-sequences may fold and give rise to deviations from the standard patterns. Our results show the coexistence of different "routes to chaos" in one and the same mathematical model and the necessity to enlarge the parameter space in both real and computer experiments on chaotic transitions.

Cooperative and chaotic transition of a free electron laser Hamiltonian model

We study a free electron laser hamiltonian model for N relativistic electrons interacting with a constant amplitude wiggler field and a laser field. As the amplitude of the wiggler field or the electron density increase above some threshold value, we find a first-order-like transition from an unbunched weakly coupled and ordered motion to a strongly coupled and self-bunched chaotic motion in which the system radiates strongly and cooperatively.

Transitions and distribution functions for chaotic systems

We study chaotic systems generated by deterministic or probablistic mappings. We introduce the density function which is an eigenfunction of a probability-preserving kernel $K$. We are able to show that all eigenvalues of $K$ have magnitude less than or equal to 1 and that the only magnitude-one eigenvalues are the $N\mathrm{th}$ roots of unity. We have also calculated the corresponding eigenfunctions associated with these magnitude-one eigenvalues: These eigenfunctions can be expanded in terms of $N$ positive functions having disjoint support. We then concentrate on a one-dimensional system, and study the behavior and mechanism for various chaotic transitions. We find that the mechanism associated with the 2 to 1 (or more generally, $2N$ to $N$) transition is different from those associated with other chaotic transitions. We then determine the conditions for these transitions, and express them in a universal form. We confirm the Huberman-Rudnick scaling in the large ${2}^{n}$ to ${2}^{n\ensuremath{-}1}$ chaotic-transition region, and determine the prefactor at these transitions. In addition, we establish a simple relation between the Lyapunov exponent and the folding of the distribution functions. We have also studied the chaotic regions of this system numerically.

Chaotic motions and transition to stochasticity in the classical problem of the heavy rigid body with a fixed point

We give numerical evidence for the existence of chaotic motions and of a transition to stochasticity in the classical problem of a heavy rigid body with a fixed point, by studying a perturbation of the Euler-Poinsot case. This gives also numerical evidence for the non-integrability of this problem.

Power spectral analysis of a dynamical system

Power spectra for chaotic transitions in three dimensions are presented for a dynamical system first proposed by Rössler. Relations between the spectra and the topology of the corresponding strange attractor are discussed.