In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a...In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a certain critical value, which is more reasonable in the physical sence compared with classical results.展开更多
We analyse the appearance of coherent motion in the dynamics of the Langevin equation in the subtle case of I<1,and show that stochastic resonance does exist even in the non-critical case I<1.Moreover,we show th...We analyse the appearance of coherent motion in the dynamics of the Langevin equation in the subtle case of I<1,and show that stochastic resonance does exist even in the non-critical case I<1.Moreover,we show the monotonicity of the rotation number and discuss the relationship between the center frequency of the power spectrum peak and the rotation number.展开更多
Turbulence modeling by use of the renormalization group （RNG） κ-ε model for Reynolds-stress closure is carried out to reveal the evolution dynamics for lock release gravity currents with the so-called slumping, in...Turbulence modeling by use of the renormalization group （RNG） κ-ε model for Reynolds-stress closure is carried out to reveal the evolution dynamics for lock release gravity currents with the so-called slumping, inviscid and viscous phases. Field evolution of the turbulent current is investigated, and time transition of global energy balance is presented between the terms of potential energy, averaged kinetic energy, turbulent kinetic energy, turbulent dissipation and viscous dissipation. It is well illustrated that turbulent dissipation and viscous force are respectively dominant in the inviscid and viscous phases, while inertia effect accounts for the slumping.展开更多
The stability of a class of delayed cellular neural networks （DCNN） with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a d...The stability of a class of delayed cellular neural networks （DCNN） with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.展开更多
文摘In this article sharper estimates on the radii of absorbing sets for the Kuramoto_Sivashinsky equation are given. It is proved that radii of absorbing sets will decay to zero as the coefficient of viscosity tends to a certain critical value, which is more reasonable in the physical sence compared with classical results.
文摘We analyse the appearance of coherent motion in the dynamics of the Langevin equation in the subtle case of I<1,and show that stochastic resonance does exist even in the non-critical case I<1.Moreover,we show the monotonicity of the rotation number and discuss the relationship between the center frequency of the power spectrum peak and the rotation number.
基金The paper was financially supported by the National Natural Science Foundation of China (Grant No.10372006)
文摘Turbulence modeling by use of the renormalization group （RNG） κ-ε model for Reynolds-stress closure is carried out to reveal the evolution dynamics for lock release gravity currents with the so-called slumping, inviscid and viscous phases. Field evolution of the turbulent current is investigated, and time transition of global energy balance is presented between the terms of potential energy, averaged kinetic energy, turbulent kinetic energy, turbulent dissipation and viscous dissipation. It is well illustrated that turbulent dissipation and viscous force are respectively dominant in the inviscid and viscous phases, while inertia effect accounts for the slumping.
基金the National Natural Science Foundation of China(No.10771155)the Special Foundation for the Authors of National Excellent Doctoral Dissertations of China(FANEDD)
文摘The stability of a class of delayed cellular neural networks （DCNN） with or without noise perturbation is studied. After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system, we further investigate the case with noise perturbation. When DCNN is perturbed by external noise, the system is globally stable. An important fact is that, when the system is perturbed by internal noise, it is globally exponentially stable only if the total noise strength is within a certain bound. This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.
