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Youming Lei, Fan Zheng
Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples...
December 2016: Chaos
Fei Liu, Jiang Wang, Chen Liu, Huiyan Li, Bin Deng, Chris Fietkiewicz, Kenneth A Loparo
An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network...
December 2016: Chaos
Aisling J Daly, Jan M Baetens, Bernard De Baets
Biodiversity has a critical impact on ecosystem functionality and stability, and thus the current biodiversity crisis has motivated many studies of the mechanisms that sustain biodiversity, a notable example being non-transitive or cyclic competition. We therefore extend existing microscopic models of communities with cyclic competition by incorporating resource dependence in demographic processes, characteristics of natural systems often oversimplified or overlooked by modellers. The spatially explicit nature of our individual-based model of three interacting species results in the formation of stable spatial structures, which have significant effects on community functioning, in agreement with experimental observations of pattern formation in microbial communities...
December 2016: Chaos
Wady A Rios Herrera, Joaquín Escalona, Daniel Rivera López, Markus F Müller
Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M...
December 2016: Chaos
Nishant Malik, Feng Shi, Hsuan-Wei Lee, Peter J Mucha
One of the fundamental structural properties of many networks is triangle closure. Whereas the influence of this transitivity on a variety of contagion dynamics has been previously explored, existing models of coevolving or adaptive network systems typically use rewiring rules that randomize away this important property, raising questions about their applicability. In contrast, we study here a modified coevolving voter model dynamics that explicitly reinforces and maintains such clustering. Carrying out numerical simulations for a variety of parameter settings, we establish that the transitions and dynamical states observed in coevolving voter model networks without clustering are altered by reinforcing transitivity in the model...
December 2016: Chaos
S Bowong, L Mountaga, A Bah, J J Tewa, J Kurths
Neisseria meningitidis (Nm) is a major cause of bacterial meningitidis outbreaks in Africa and the Middle East. The availability of yearly reported meningitis cases in the African meningitis belt offers the opportunity to analyze the transmission dynamics and the impact of control strategies. In this paper, we propose a method for the estimation of state variables that are not accessible to measurements and an unknown parameter in a Nm model. We suppose that the yearly number of Nm induced mortality and the total population are known inputs, which can be obtained from data, and the yearly number of new Nm cases is the model output...
December 2016: Chaos
Yutaka Shimada, Emiko Takagi, Tohru Ikeguchi
We observe a symmetry of Lyapunov exponents in bifurcation structures of one-dimensional maps in which there exists a pair of parameter values in a dynamical system such that two dynamical systems with these paired parameter values have the same Lyapunov exponent. We show that this is a consequence of the presence of an invariant transformation from a dynamical system with one of the two paired parameter values to that with another parameter value, which does not change natures of dynamical systems.
December 2016: Chaos
José M Amigó, Yoshito Hirata, Kazuyuki Aihara
The ignorance score measures the quality of probabilistic forecasting. In this paper, we study its basic properties in the perfect model scenario, i.e., under the assumption that the system producing the data is perfectly known. Two further qualifications are added to this general setting. First, the system is a discrete-time, measure-preserving dynamical system. Moreover, randomness results from the quantization of the state space (i.e., from the finite precision of the observations), rather than being introduced via observational noise...
December 2016: Chaos
Arnab Basak, Krishna Kumar
Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number Pr = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical direction or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous gluing of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ( Q≤5)...
December 2016: Chaos
Michael McCullough, Konstantinos Sakellariou, Thomas Stemler, Michael Small
It has been established that the count of ordinal patterns, which do not occur in a time series, called forbidden patterns, is an effective measure for the detection of determinism in noisy data. A very recent study has shown that this measure is also partially robust against the effects of irregular sampling. In this paper, we extend said research with an emphasis on exploring the parameter space for the method's sole parameter-the length of the ordinal patterns-and find that the measure is more robust to under-sampling and irregular sampling than previously reported...
December 2016: Chaos
Nina Sviridova, Kazuyuki Nakamura
Noise contamination in experimental data with underlying chaotic dynamics is one of the significant problems limiting the application of many nonlinear time series analysis methods. Although numerous studies have been devoted to the investigation of different aspects of noise-nonlinear dynamics interactions, the effects produced by noise on chaotic dynamics are not fully understood. This study sought to analyze the local effects produced by noise on chaotic dynamics with a smooth attractor. Local Wayland test translation errors were calculated for noise-induced Lorenz and Rössler chaotic models, and for experimental green light photoplethysmogram data...
December 2016: Chaos
Konstantinos Sakellariou, Michael McCullough, Thomas Stemler, Michael Small
We are motivated by real-world data that exhibit severe sampling irregularities such as geological or paleoclimate measurements. Counting forbidden patterns has been shown to be a powerful tool towards the detection of determinism in noisy time series. They constitute a set of ordinal symbolic patterns that cannot be realised in time series generated by deterministic systems. The reliability of the estimator of the relative count of forbidden patterns from irregularly sampled data has been explored in two recent studies...
December 2016: Chaos
M Sala, J C Leitão, E G Altmann
We propose new methods to numerically approximate non-attracting sets governing transiently chaotic systems. Trajectories starting in a vicinity Ω of these sets escape Ω in a finite time τ and the problem is to find initial conditions x∈Ω with increasingly large τ=τ(x). We search points x' with τ(x')>τ(x) in a search domain in Ω. Our first method considers a search domain with size that decreases exponentially in τ, with an exponent proportional to the largest Lyapunov exponent λ1. Our second method considers anisotropic search domains in the tangent unstable manifold, where each direction scales as the inverse of the corresponding expanding singular value of the Jacobian matrix of the iterated map...
December 2016: Chaos
Thotreithem Hongray, Janaki Balakrishnan
A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in this forced system with dynamic feedback. We show that the bursting oscillations are caused because of a transition of the quiescent state to the spiking state by a saddle-focus bifurcation, and because of another saddle-focus bifurcation, which leads to cessation of spiking, bringing the system back to the quiescent state...
December 2016: Chaos
Andrey Gavrilov, Dmitry Mukhin, Evgeny Loskutov, Evgeny Volodin, Alexander Feigin, Juergen Kurths
We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales...
December 2016: Chaos
Alvaro Diaz-Ruelas, Henrik Jeldtoft Jensen, Duccio Piovani, Alberto Robledo
It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems...
December 2016: Chaos
Evgeny Gromov, Boris Malomed
One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schrödinger equation for intense HF waves to the Boussinesq (Bq) or Korteweg-de Vries (KdV) equation for the LF component through quadratic terms. The systems apply, in particular, to the interaction of surface (HF) and internal (LF) waves in stratified fluids. These solutions are two-component generalizations of the single-component Bq and KdV solitons...
December 2016: Chaos
H T Li, J Zu, Y F Yang, W Y Qin
Snap-through is used to improve the efficiencies of energy harvesters and extend their effective frequency bandwidths. This work uses the Melnikov method to explore the underlying snap-through mechanism and the conditions necessary for homoclinic bifurcations in a magnet-induced buckled energy harvester. First, an electromechanical model of the energy harvester is established analytically using the Euler-Bernoulli beam theory and the extended Hamilton's principle. Second, the Melnikov function of the model is derived, and the necessary conditions for homoclinic bifurcations and chaos are presented on the basis of this model...
December 2016: Chaos
Wenchang Zhou, Yong Zou, Jie Zhou, Zonghua Liu, Shuguang Guan
Recently, the Bellerophon state, which is a quantized, time dependent, clustering state, was revealed in globally coupled oscillators [Bi et al., Phys. Rev. Lett. 117, 204101 (2016)]. The most important characteristic is that in such a state, the oscillators split into multiple clusters. Within each cluster, the instantaneous frequencies of the oscillators are not the same, but their average frequencies lock to a constant. In this work, we further characterize an intermittent Bellerophon state in the frequency-weighted Kuramoto model with a biased Lorentzian frequency distribution...
December 2016: Chaos
Jordane Preto
Almost five decades ago, H. Fröhlich [H. Fröhlich, "Long-range coherence and energy storage in biological systems," Int. J. Quantum Chem. 2(5), 641-649 (1968)] reported, on a theoretical basis, that the excitation of quantum modes of vibration in contact with a thermal reservoir may lead to steady states, where under high enough rate of energy supply, only specific low-frequency modes of vibration are strongly excited. This nonlinear phenomenon was predicted to occur in biomolecular systems, which are known to exhibit complex vibrational spectral properties, especially in the terahertz frequency domain...
December 2016: Chaos
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