We solve the general-relativistic steady-state eigenvalue problem of neutrino-driven protoneutron star winds, which immediately follow core-collapse supernova explosions. We provide velocity, density, temperature, and composition profiles and explore the systematics and structures generic to such a wind for a variety of protoneutron star characteristics. Furthermore, we derive the entropy, dyna...

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...

Markov models are widely used to describe stochastic dynamics. Here, we show that Markov models follow directly from the dynamical principle of maximum caliber (Max Cal). Max Cal is a method of deriving dynamical models based on maximizing the path entropy subject to dynamical constraints. We give three different cases. First, we show that if constraints (or data) are given in the form of singl...

Cortical networks are dynamical systems whose task is to process information. However, in addition to 'intended' dynamical behaviors, the sheer complexity of a cortical network's structure-regardless of its precise details-should generate additional 'unintended' dynamical behaviors. Dynamics observed in cortical network models and in the somatosensory cortex suggest that such spurious dynamical...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems are giv...