Equivalent conditions on periodic feedback stabilization for linear periodic evolution equations

This paper studies the periodic feedback stabilization for a class of linear T  -periodic evolution equations. Several equivalent conditions on the linear periodic feedback stabilization are obtained. These conditions are related to the following subjects: the attainable subspace of the controlled evolution equation under consideration; the unstable subspace (of the evolution equation with the null control) provided by the Kato projection; the Poincaré map associated with the evolution equation with the null control; and two unique continuation properties for the dual equations on different time horizons [0,T]$[0,T]$ and [0,_n0T]$[0,n_{0}T]$ (where _n0$n_0$ is the sum of algebraic multiplicities of distinct unstable eigenvalues of the Poincaré map). It is also proved that a T-periodic controlled evolution equation is linear T-periodic feedback stabilizable if and only if it is linear T-periodic feedback stabilizable with respect to a finite-dimensional subspace. Some applications to heat equations with time-periodic potentials are presented.     

Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains

This paper is concerned with pullback attractors of the stochastic p  -Laplace equation defined on the entire space Rⁿ${\mathbb{R}}^n$. We first establish the asymptotic compactness of the equation in L²(Rⁿ)$L^2({\mathbb{R}}^n)$ and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on Rⁿ${\mathbb{R}}^n$ is overcome by the uniform smallness of solutions outside a bounded domain.     

On optimal periodic dividend strategies in the dual model with diffusion

The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximizes the expected present value of dividends paid until ruin. Interestingly, a ‘liquidation-at-first-opportunity’ strategy is optimal in some cases where the surplus process has a positive drift. Results are illustrated.     

Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics简

In this paper, the complicated dynamics is studied near a double homoclinic loops with bellows configuration for general systems. For the non-twisted multiple homoclinics, the existence of periodic orbit with the specified route and the existence of shift-invariant curve sequences defined on the cross sections of multiple homoclinics corresponding to any specified one-side infinite sequences are given. In addition, the existence regions are also located.     

Existence theorems for some abstract nonlinear non-autonomous systems with delays

For some abstract classes of nonlinear non-autonomous systems with variable and state-dependent delays existence, non-existence and multiplicity of periodic solutions are discussed. To illustrate the efficiency of the method, we obtain some well-known results for applied systems as corollaries of our existence theorems.     

The effects of time delay on the stochastic resonance in feed-forward-loop neuronal network motifs

The dependence of stochastic resonance in the feed-forward-loop neuronal network motifs on the noise and time delay are studied in this paper. By computational modeling, Izhikevich neuron model with the chemical coupling is used to build the triple-neuron feed-forward-loop motifs with all possible motif types. Numerical results show that the correlation between the periodic subthreshold signal’s frequency and the dynamical response of the network motifs is resonantly dependent on the intensity of additive spatiotemporal noise. Interestingly, the excitatory intermediate neuron could induce intermittent stochastic resonance, whereas the inhibitory one weakens its influence on the intermittent mode. More importantly, it is found that the increasing delays can induce the intermittent appearance of regions of stochastic resonance. Based on the effects of the time delay on the stochastic resonance, the reasons and conditions of such intermittent resonance phenomenon are analyzed.