Effects of Self-Correlation Time and Cross-Correlation Time of Additive and Multiplicative Colored Noises for Dynamical Properties of a Bistable System

Considering a bistable system driven by additive and multiplicative colored noises with colored cross-correlation, we obtain the analytic expressions of the stationary probability distribution P _st(x), the linear relaxation time T _c , and the correlated function C(s). The effects of the noise intensity, the self-correlation time and the cross-correlation time for the bistable system are discussed. The noise intensity D speeds up relaxation of the system from unstable points, which when D < Q, the effects are the most obvious; when D > Q, the effects are damped. The self-correlation time τ₁ and τ₂ make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x. On the contrary, the cross-correlation time τ₃ makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x. The effect of the self-correlation time is more projecting than the effect of the cross-correlation time. PACS number: 05.40.−a, 02.50.−r, 05.10.Gg.     

Post-buckling behavior of a fixed arch for variable geometry structures

The behavior of a bistable strut for variable geometry structures was investigated in this paper. A fixed shallow arch subjected to a central concentrated load was used to study the equilibrium path of the bistable strut. Based on a nonlinear strain–displacement relationship, the critical loads for both the symmetric snap-through and asymmetric bifurcation buckling modes were obtained. Moreover, the principal of virtual work was also used to establish the post-buckling differential equilibrium equations of the arch in the horizontal and vertical directions. Therefore, the whole mechanical behavior before and after the buckling of fixed arches is investigated.     

Influence of two-photon absorption on bistable switching in a silicon photonic crystal microcavity

By employing a simplified nonlinear coupled mode theory, we discuss the influence of two-photon absorption (TPA) on the characteristics of bistable switching. It is revealed that the critical value of frequency detuning for bistability rises linearly with increasing TPA coefficient k (when k is less than 30), and eventually access to a saturated value. It is also found that TPA effect will be enhanced for a greater frequency detuning, especially when transmission reaches its peak value. As a result, the peak transmission will decrease monotonously with the increasing frequency detuning. Based on this simplified model, the TPA-induced temperature rise in microcavity is also estimated. The theoretical predictions show good agreement with the simultaneous results, as well as the proposed experimental phenomena.     

Bistable traveling waves for a competitive–cooperative system with nonlocal delays

This paper is devoted to the study of bistable traveling waves for a competitive–cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach.     

An analysis of interacting bistable magnetic microwires: from ordered to chaotic behaviours

Fe-based magnetostrictive amorphous wires are bistable exhibiting square-shaped longitudinal hysteresis loops. This is a consequence of their particular domain structure that allows them to be approached as magnetic dipoles. Arrays of such bistables wires are accordingly shown to be coupled by magnetostatic interactions. Furthermore, an analysis of these interactions allows us to conclude that depending on the relative strength of the magnetostatic and Zeeman interactions, ordered, complex or chaotic behaviours are found in the temporal variation of the array magnetisation.     

Mean first-passage time in a bistable system driven by multiplicative and additive colored noises with colored cross-correlation

The effect of any system parameter (include p, q, λ, τ₁, τ₂, τ₃) on the mean first-passage time is investigated in a symmetric bistable system driven by multiplicative and additive colored noise with colored cross-correlation. Expression of the mean first-passage time (MFPT) has been obtained by applying the steepest-descent approximation. The effects of the additive noise intensity and the multiplicative noise intensity on the MFPT are mostly different only with bigger positive values of the strength of correlations between multiplicative and additive noise; and the MFPT has a maximum with the increase of the multiplicative noise intensity. The effects of the noise self-correlation times on the MFPT are quite different from that of the correlation time between the noises as the strength of correlations between multiplicative and additive noise is positive.     

From molecular to continuum modelling of bistable liquid crystal devices

We study nematic equilibria on a square with tangent Dirichlet conditions on the edges, in three different modelling frameworks: (i) the off-lattice Hard Gaussian Overlap and Gay–Berne models; (ii) the lattice-based Lebwohl–Lasher model; and the (iii) two-dimensional Landau-de Gennes model. We compare the modelling predictions, identify regimes of agreement and in the Landau-de Gennes case, find up to 21 different equilibria. Of these, two are physically stable.     

A novel computer virus model and its dynamics

In this paper, we propose a novel computer virus propagation model and study its dynamic behaviors; to our knowledge, this is the first time the effect of anti-virus ability has been taken into account in this way. In this context, we give the threshold for determining whether the virus dies out completely. Then, we study the existence of equilibria, and analyze their local and global asymptotic stability. Next, we find that, depending on the anti-virus ability, a backward bifurcation or a Hopf bifurcation may occur. Finally, we show that under appropriate conditions, bistable states may be around. Numerical results illustrate some typical phenomena that may occur in the virus propagation over computer network.     

Electrical bistability of tris-(8-hydroxyquinoline) aluminum (Alq3)/ZnSe organic-inorganic bistable device

We present that the electrical bistability in organic-inorganic bistable devices based on tris-(8-hydroxyquinoline) aluminum (Alq₃) and zinc selenide (ZnSe) with the tri-layer structure of Alq₃/aluminum (Al)/ZnSe. The current-voltage characteristics of the bistable device exhibit two electrical states as low (OFF state) and high (ON state) conductivity with ON/OFF ratio about four orders of magnitude. The conduction mechanisms in both ON and OFF states were analyzed by theoretical model. In the OFF state, the conduction mechanisms can be explained by thermionic emission model, which the ON state can be described by ohmic conduction model. The retention times of both states are more than 8000 s, and the device can reproduce continuous write-read-erase-read switching cycles. Moreover, for the organic-inorganic bistable device was kept at one year in ambient condition without encapsulation. The device still exhibited the electrical bistable behavior. Consequently, the ZnSe layer may be led to improve the lifetime property of the bistable device which acted as a self-encapsulating layer.     

Spatial disorder and pattern formation in lattices of coupled bistable elements

The spatio-temporal dynamics of discrete lattices of coupled bistable elements is considered. It is shown that both regular and chaotic spatial field distributions can be realized depending on parameter values and initial conditions. For illustration, we provide results for two lattice systems: the FitzHugh-Nagumo model and a network of coupled bistable oscillators. For the latter we also prove the existence of phase clusters, with phase locking of elements in each cluster.