A p-Laplacian equation with weak Allee effect growth rate and Dirichlet boundary condition is considered. The existence, multiplicity and bifurcation of positive solutions are proved with comparison and variational techniques. The existence of multiple positive solutions implies that the related ecological system may exhibit bistable dynamics.

We have experimentally investigated dynamical hysteresis behavior by changing the sweeping frequency of the cavity input field in the optical bistability of rubidium atoms (in a three-level atomic-type configuration) inside an optical cavity. The shape, width (or area), and direction of the hysteresis cycle are sensitive functions of the sweeping frequency for such an optical bistable system.

We report on the experimental observation of coherence resonance in a bistable system with delay. Our system consists of a vertical-cavity surface-emitting laser subject to time-delayed optical feedback simultaneously from a long and from an extremely short external cavity. Coherence resonance is experimentally proven by analysis of the residence time distribution of the polarization mode-hoppi...

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. For this purpose, we have considered two types of modulations, namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is present, irrespective of whether the system is monostable or bistable.

The abrupt and irreversible transition from interphase to M phase is essential to separate DNA replication from chromosome segregation. This transition requires the switch-like phosphorylation of hundreds of proteins by the cyclin-dependent kinase 1 (Cdk1):cyclin B (CycB) complex. Previous studies have ascribed these switch-like phosphorylations to the auto-activation of Cdk1:CycB through the r...

There have been a growing number of observations of oscillating protein levels (p53 and NFkB) in eukaryotic signalling pathways. This has resulted in a renewed interest in the mechanism by which such oscillations might occur. Recent computational work has shown that a multisite phosphorylation mechanism such as that found in the MAPK cascade can theoretically exhibit bistability. The bistable b...

For a microelectromechanical (MEM) resonator, the combination of mechanical nonlinearity and electrical driving force can lead to bistability. In such a case, the system exhibits two coexisting stable oscillatory states (attractors): one with low and another with high energy. Under the influence of noise, with high probability the system can be perturbed into the low-energy state. We propose a ...

The synchronization induced by suprathreshold inputs with the spatial variability has been discussed in N -unit coupled bistable Langevin models subjected to cross-correlated additive and multiplicative noise. We have employed numerical simulations and the semi-analytic augmented moment method (AMM) which is the second-order moment approximation for local and global variables [H. Hasegawa, Phys...

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochas...

We theoretically study the impact of an external noise on a kinetic mean-field model for the bistable catalytic CO oxidation on Pd(111) surfaces. A spatially homogeneous Gaussian white noise is imposed on the fraction of CO in the constant gas flow directed at the surface and the resulting stochastic system is analyzed by a set of Langevin equations. Using an adiabatic elimination technique, we...