Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two rep... more The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Journal of computational and applied mathematics, Jan 15, 2014
Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeli... more Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex ...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
The stability of synchronous chaos of coupled oscillators with diffusive and gradient couplings i... more The stability of synchronous chaos of coupled oscillators with diffusive and gradient couplings is investigated. The stability boundaries of all transverse modes can be simultaneously drawn by justifying the boundary of a single mode, according to a scaling relation. Therefore, the distribution of stable and unstable regions can be explicitly shown in control parameter space. Bifurcations through different unstable modes, leading to different spatial orders, are analyzed.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Network of coupled oscillators has long been employed as an important approach to explore the com... more Network of coupled oscillators has long been employed as an important approach to explore the complicated dynamics in spatially extended systems. Here we show how this approach can be used to the analysis of turbulence pinning control. Specifically, by use of a model of two-dimensional drift-wave plasma turbulence, we investigate how the performance of the turbulence control is influenced by the spatial distribution of the pinning strength. It is found that the dynamics of pinned turbulence can be well captured by a simple model of networked modes, based on which the dependence of the control performance on the pinning distribution can be analytically obtained. In particular, the model predicts that as the distribution of the pinning strength becomes more nonuniform, the performance of turbulence control will be gradually decreased. This theoretical prediction is in good agreement with the results of numerical simulations, including the sinusoidal and localized pinning distributions...
Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigat... more Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigated based on numerical computation of two coupled phi(4) equations. Some relevant quantities such as the bare energies, the interaction energy, and the phase difference of the two oscillators are computed to clarify the characteristics of the transitions and the measure-synchronous states. A bifurcation with discontinuous bare energy and continuous interaction energy, which takes the maximum value at the critical point, is found for the transition from the desynchronous quasiperiodic state to the measure-synchronous quasiperiodic state, and the related power law scalings are deduced. Stick-slip and random-walk-like behavior of the phase difference is found for the chaotic measure-synchronous state, and this explains the monotonous increase of the interaction energy with an increase of coupling.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two rep... more The effects of amplitude-dependent coupling on oscillator death (OD) are investigated for two repulsively coupled Lorenz oscillators. Based on numerical simulations, it is shown that as constraint strengths on the amplitude-dependent coupling change, an oscillatory state may undergo a transition to an OD state. The parameter regimes of the OD domain are theoretically determined, which coincide well with the numerical results. An electronic circuit is set up to exhibit the transition process to the OD state with an amplitude-dependent coupling. These findings may have practical importance on chaos control and oscillation depression.
Journal of computational and applied mathematics, Jan 15, 2014
Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeli... more Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex ...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
The stability of synchronous chaos of coupled oscillators with diffusive and gradient couplings i... more The stability of synchronous chaos of coupled oscillators with diffusive and gradient couplings is investigated. The stability boundaries of all transverse modes can be simultaneously drawn by justifying the boundary of a single mode, according to a scaling relation. Therefore, the distribution of stable and unstable regions can be explicitly shown in control parameter space. Bifurcations through different unstable modes, leading to different spatial orders, are analyzed.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2014
Network of coupled oscillators has long been employed as an important approach to explore the com... more Network of coupled oscillators has long been employed as an important approach to explore the complicated dynamics in spatially extended systems. Here we show how this approach can be used to the analysis of turbulence pinning control. Specifically, by use of a model of two-dimensional drift-wave plasma turbulence, we investigate how the performance of the turbulence control is influenced by the spatial distribution of the pinning strength. It is found that the dynamics of pinned turbulence can be well captured by a simple model of networked modes, based on which the dependence of the control performance on the pinning distribution can be analytically obtained. In particular, the model predicts that as the distribution of the pinning strength becomes more nonuniform, the performance of turbulence control will be gradually decreased. This theoretical prediction is in good agreement with the results of numerical simulations, including the sinusoidal and localized pinning distributions...
Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigat... more Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigated based on numerical computation of two coupled phi(4) equations. Some relevant quantities such as the bare energies, the interaction energy, and the phase difference of the two oscillators are computed to clarify the characteristics of the transitions and the measure-synchronous states. A bifurcation with discontinuous bare energy and continuous interaction energy, which takes the maximum value at the critical point, is found for the transition from the desynchronous quasiperiodic state to the measure-synchronous quasiperiodic state, and the related power law scalings are deduced. Stick-slip and random-walk-like behavior of the phase difference is found for the chaotic measure-synchronous state, and this explains the monotonous increase of the interaction energy with an increase of coupling.
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