Results 1 - 10 of 25
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[en] We use the Melnikov method to identify chaotic behavior in geodesic motion perturbed by the minimal length effects around a Schwarzschild black hole. Unlike the integrable unperturbed geodesic motion, our results show that the perturbed homoclinic orbit, which is a geodesic joining the unstable circular orbit to itself, becomes chaotic in the sense that Smale horseshoes chaotic structure is present in phase space.
[en] Aiming to solve the problems of low accuracy of multi-step prediction and difficulty in determining the maximum number of prediction steps of chaotic time series, a multi-step time series prediction model based on the dilated convolution network and long short-term memory (LSTM), named the dilated convolution-long short-term memory (DC-LSTM), is proposed. The dilated convolution operation is used to extract the correlation between the predicted variable and correlational variables. The features extracted by dilated convolution operation and historical data of predicted variable are input into LSTM to obtain the desired multi-step prediction result. Furthermore, cross-correlation analyses (CCA) are applied to calculate the reasonable maximum prediction steps of chaotic time series. Actual applications of multi-step prediction were studied to demonstrate the effectiveness of the proposed model which has superiorities in RMSE, MAE and prediction accuracy because of the extraction of correlation between the predicted variable and correlational variables. Moreover, the proposed DC-LSTM model provides a new method for prediction of chaotic time series and lays a foundation for scientific data analysis of chaotic time series monitoring systems.
[en] We show theoretically that a lattice of exciton-polaritons can behave as a life-like cellular automaton when simultaneously excited by a continuous wave coherent field and a time-periodic sequence of non-resonant pulses. This provides a mechanism of realizing a range of highly sought spatiotemporal structures under the same conditions, including: discrete, oscillating, and rotating solitons; breathers; soliton trains; guns; and chaotic behaviour. These structures can survive in the system indefinitely, despite the presence of dissipation and disorder, and allow universal computation. (paper)
[en] Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly rich and so far remains underexplored. Works devoted to this subject have typically focussed on dissipation constants which are substantially larger than those encountered in current experiments, such that the nonlinear dynamics of weakly dissipative optomechanical systems is almost uncharted waters. In this work, we fill this gap and investigate the regular and chaotic dynamics in this important regime. To analyze the dynamical attractors, we have extended the ‘generalized alignment index’ method to dissipative systems. We show that, even when chaotic motion is absent, the dynamics in the weakly dissipative regime is extremely sensitive to initial conditions. We argue that reducing dissipation allows chaotic dynamics to appear at a substantially smaller driving strength and enables various routes to chaos. We identify three generic features in weakly dissipative classical optomechanical nonlinear dynamics: the Neimark–Sacker bifurcation between limit cycles and limit tori (leading to a comb of sidebands in the spectrum), the quasiperiodic route to chaos, and the existence of transient chaos. (paper)
[en] This paper gives multiswitching synchronisation scheme for a class of fractional-order chaotic systems by combining active and adaptive control theories. Adaptive controllers have been designed by using different laws of switching and fractional-order Lyapunov stability theory. We have also constructed a new fractional-order Duffing system. The fractional-order Duffing system and fractional-order Rabinovich–Fabrikant system have been taken as the drive system and the response system respectively. Applications have been demonstrated. Theoretical analysis and numerical simulations are also given to verify the robustness of the proposed controllers. (author)
[en] Motivated by the recent gravitational wave detection by the LIGO–VIRGO observatories, we study the Love number and dimensionless tidal polarizability of highly magnetized stars. We also investigate the fundamental quasi-normal mode of neutron stars subject to high magnetic fields. To perform our calculations we use the chaotic field approximation and consider both nucleonic and hyperonic stars. As far as the fundamental mode is concerned, we conclude that the role played by the constitution of the stars is far more relevant than the intensity of the magnetic field, and if massive stars are considered, the ones constituted by nucleons only present frequencies somewhat lower than the ones with hyperonic cores. This feature that can be used to point out the real internal structure of neutron stars. Moreover, our studies clearly indicate that strong magnetic fields play a crucial role in the deformability of low mass neutron stars, with possible consequences on the interpretation of the detected gravitational waves signatures.
[en] Meminductor is a novel nonlinear inductor with memory. A meminductor-based chaotic oscillating circuit that has only two linear resistors, two linear capacitors and a meminductor, is designed based on a mathematical model of the flux-controlled meminductor to study its characteristics in nonlinear circuit. Through the analysis of bifurcations, dynamic map and Lyapunov exponents, it is found that the system can exhibit some complex characteristics, such as an infinite number of equilibrium points and burst chaos. Especially, bifurcation without parameters and coexisting attractors appear under a fixed set of parameter values but different initial conditions. Moreover, random characteristics of the PN sequences generated from the chaotic circuit are tested via the test suit of National Institute of Standards and Technology (NIST), and the tested randomness definitely reaches the standards of NIST. Finally, a scheme for digitally realising this oscillating circuit is provided using the digital signal processor (DSP). (author)
[en] A memristive chaotic system of rotational symmetry is constructed and analysed. The dynamical behaviour of the system is demonstrated by phase trajectories, Lyapunov exponents and bifurcation diagrams. Coexisting attractors are observed and a simple approach for amplitude control is proposed according to the specific structure. It shows that this symmetric memristive system has partial amplitude control when a control function is introduced. The corresponding circuit implementation is given by generating a symmetric pair of chaotic attractors. Circuit results agree well with the theoretical analysis and numerical simulation. (author)
[en] We investigate Bloch–Zener oscillations and mean-field Bloch bands of a Bose–Einstein condensate (BEC) in a Lieb optical lattice. We find that the atomic interaction will break the point group symmetry of the system, leading to the destruction of the Dirac cone structure, while the flat band is preserved on the highly symmetric lines. Due to the nonlinear effect, a tubular band structure with a flat band will appear in the system. Furthermore, comparing with that the tight-binding (TB) model fails to describe the interacting bosonic systems in the honeycomb lattice, we show that the TB model is applicable to study the nonlinear energy band structures for the Lieb lattice. In addition, we show that the loop structure can be determined by the observation of the chaos of the state in the Bloch–Zener oscillations. (paper)
[en] We compare the entire classical and quantum evolutions of the Dicke model in its regular and chaotic domains. This is a paradigmatic interacting spin-boson model of great experimental interest. By studying the classical and quantum survival probabilities of initial coherent states, we identify features of the long-time dynamics that are purely quantum and discuss their impact on the equilibration times. We show that the ratio between the quantum and classical asymptotic values of the survival probability serves as a metric to determine the proximity to a separatrix in the regular regime and to distinguish between two manifestations of quantum chaos: scarring and ergodicity. In the case of maximal quantum ergodicity, our results are analytical and show that quantum equilibration takes longer than classical equilibration. (paper)