How can neural circuits maintain stable activity states when they are constantly being modified by Hebbian processes that are notorious for being unstable? A new synaptic plasticity mechanism is presented here that enables a neuron to obtain homeostasis of its firing rate over longer timescales while leaving the neuron free to exhibit fluctuating dynamics in response to external inputs. Mathema...

We discuss two types of instabilities which may arise in string theory compactified to asymptotically AdS spaces: perturbative, due to discrete modes in the spectrum of the Laplacian, and non-perturbative, due to brane nucleation. In the case of three dimensional Einstein manifolds, we completely characterize the presence of these instabilities, and in higher dimensions we provide a partial cla...

We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R0 exceeds one, while the trivial equilibrium and the disease-free equilibrium a...

In this paper, some results of feedback stabilization on compacta for a nonlinear control system are obtained by using an invariant manifold approach. In particular, a class of globally nonminimum phase systems are treated. Issues such as high gain feedback stabilization on compacta vs. peaking phenomenon, and globally exponentially minimum phase vs. globally asymptotically (critically) minimum...

The global dynamics of discrete competitive model of Lotka-Volterra type with two species is considered. Earlier works have shown that the unique positive equilibrium is globally attractive under the assumption that the intrinsic growth rates of the two competitive species are less than 1 ln 2, and further the unique positive equilibrium is globally asymptotically stable under the stronger cond...

In this paper, we present a new result that allows for studying the global stability of disease-free equilibrium point when basic reproduction number is less than 1, in fractional calculus context. The method only involves linear algebra and can be easily applied to study asymptotic stability. After proving some auxiliary lemmas involving Mittag–Leffler function, main paper. Under assumptions, ...

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4 T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types o...

We propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations DDEs that describes the interaction of the virus with two classes of target cells. The second model is a 2n 1 -dimensional system of nonlinear DDEs that describes the dynamics o...