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Register a new userEmergence of coexisting coherence and incoherence by an external forcing
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Added by
Ramachandran Suresh
Publication date
2015
fields
Physics
and research's language is
English
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A common external forcing can cause a saddle-node bifurcation in an ensemble of identical Duffing oscillators by breaking the symmetry of the individual bistable (double-well) unit. The strength of the forcing determines the separation between the saddle and node, which in turn dictates different dynamical transitions depending on the distribution of the initial states of the oscillators. In particular, chimera-like states appear in the vicinity of the saddle-node bifurcation for which theoretical explanation is provided from the stability of slow-scale dynamics of the original system of equations. Further, as a consequence, it is shown that even a linear nearest neighbor coupling can lead to the manifestation of the chimera states in an ensemble of identical Duffing oscillators in the presence of the common external forcing.
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We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the mean-field of the oscillators below it in the hierarchy, and couples diffusively to the oscillator above it in the hierarchy. We find that coupling to one dissimilar external system manages to suppress the chaotic dynamics of all the oscillators in the network at sufficiently high coupling strength. This holds true irrespective of whether the connection to the external system is direct or indirect through oscillators at another level in the hierarchy. Investigating the synchronization properties show that the oscillators have the same steady state at a particular level of hierarchy, whereas the steady state varies across different hierarchical levels. We quantify the efficacy of control by estimating the fraction of random initial states that go to fixed points, a measure analogous to basin stability. These quantitative results indicate the easy controllability of hierarchical networks of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.
In this paper non-linear dynamics of a periodically forced excitable glow discharge plasma has been studied. The experiments were performed in glow discharge plasma where excitability was achieved for suitable discharge voltage and gas pressure. The plasma was first perturbed by a sub-threshold sawtooth periodic signal, and we obtained small sub-threshold oscillations. These oscillations showed resonance when the frequency of the perturbation was around the characteristic frequency the plasma, and hence may be useful to estimate characteristic of an excitable system. On the other hand, when the perturbation was supra-threshold, system showed frequency entrainments. We obtained harmonic frequency entrainments for perturbation frequency greater than the characteristic frequency of the system and for lesser than the characteristic frequency, system showed only excitable behaviour.
Correlations between electrons and the effective dimensionality are crucial factors that shape the properties of an interacting electron system. For example, the onsite Coulomb repulsion, U, may inhibit, or completely block the intersite electron hopping, t, and depending on the ratio U/t, a material may be a metal or an insulator. The correlation effects increase as the number of allowed dimensions decreases. In 3D systems, the low energy electronic states behave as quasiparticles (QP), while in 1D systems, even weak interactions break the quasiparticles into collective excitations. Dimensionality is particularly important for a class of new exotic low-dimensional materials where 1D or 2D building blocks are loosely connected into a 3D whole. Small interactions between the blocks may induce a whole variety of unusual transitions. Here, we examine layered systems that in the direction perpendicular to the layers display a crossover from insulating-like, at high temperatures, to metallic-like character at low temperatures, while being metallic over the whole temperature range within the layers. We show that this change in effective dimensionality correlates with the existence or non-existence of coherent quasiparticles within the layers.
We present the results of $^{75}$As nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and resistivity measurements in KFe$_2$As$_2$ under pressure ($p$). The temperature dependence of the NMR shift, nuclear spin-lattice relaxation time ($T_1$) and resistivity show a crossover between a high-temperature incoherent, local-moment behavior and a low-temperature coherent behavior at a crossover temperature ($T^*$). $T^*$ is found to increase monotonically with pressure, consistent with increasing hybridization between localized $3d$ orbital-derived bands with the itinerant electron bands. No anomaly in $T^*$ is seen at the critical pressure $p_{rm c}=1.8$ GPa where a change of slope of the superconducting (SC) transition temperature $T_{rm c}(p)$ has been observed. In contrast, $T_{rm c}(p)$ seems to correlate with antiferromagnetic spin fluctuations in the normal state as measured by the NQR $1/T_1$ data, although such a correlation cannot be seen in the replacement effects of A in the AFe$_2$As$_2$ (A= K, Rb, Cs) family. In the superconducting state, two $T_1$ components are observed at low temperatures, suggesting the existence of two distinct local electronic environments. The temperature dependence of the short $T_{rm 1s}$ indicates nearly gapless state below $T_{rm c}$. On the other hand, the temperature dependence of the long component 1/$T_{rm 1L}$ implies a large reduction in the density of states at the Fermi level due to the SC gap formation. These results suggest a real-space modulation of the local SC gap structure in KFe$_2$As$_2$ under pressure.
We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.
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