Complete dynamical analysis of myocardial cell exposed to magnetic flux

The heart is the essential, yet complex, component of the human cardiovascular system. In the past few decades, researchers have taken giant steps toward better understanding of the cardiac system and there have been proposed some mathematical models to describe the heart's function. In this paper, a new Fitzhugh-Nagumo neuron (FNN) model is proposed to model the electrical activity of the heart in which the effect of magnetic flux is considered. Magnetic field can greatly affect the heart's function. The dynamical analyses of the model, including quantitative assessment of the system's equilibria and its stability, phase portraits analysis, bifurcation and Lyapunov exponents analysis, and basin of attraction analysis, are carried out. In addition, a model of cardiac tissue is designed to study the electrical spatiotemporal activity of heart tissue under the electromagnetic effects. Our numerical simulations confirm that the electromagnetic excitation can change the normal rhythm of the heart. It can initiate the reentrant excitations leading to emergence of spiral seeds. This study highlights the role of electromagnetic induction in dynamical instability of the action potential duration, and thus the chaotic dynamics in the cardiac tissue.     

Thermal fluctuations of dyadosphere of Reissner-Nordström,Janis-Newman-Winicour and f(R) global monopole black holes

In this paper, we study the effects of thermal fluctuations on Dyadosphere of Reissner-Nordström, Janis-Newman-Winicour and the fragmentation of f(R) global monopole black holes. In the presence of these fluctuations, we obtain various thermodynamic quantities like pressure, entropy, specific heat, Canonical and Grand Canonical ensembles. We discuss the stability of these black holes using the γ (the ratio of heat capacities). We also discuss the phase transition and range of local and global stability. It is demonstrated that in Dyadoshpere of Reissner-Nordström, Janis-Newman-Winicour and fragmentation of f(R) global monopole black holes become locally and globally stable due to logarithmic correction term and large horizon radius.     

Advantage of Quantum Theory over Nonclassical Models of Communication

Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However, a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in “space-like” and/or “time-like” paradigms. In this letter, a communication task involving three spatially separated parties is proposed where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. This task is called authentication with limited communication, the restrictions on communication being: i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several nonclassical theories although they might possess stronger “space-like” and/or “time-like” correlations. Surprisingly, quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other nonclassical strategies.     

Upper Bound of the Number of Zeros for Abelian Integrals in a Kind of Quadratic Reversible Centers of Genus One

By using the methods of Picard-Fuchs equation and Riccati equation, we study the upper bound of the number of zeros for Abelian integrals in a kind of quadratic reversible centers of genus one under polynomial perturbations of degree $n$. We obtain that the upper bound is $7[(n-3)/2]+5$ when $n\ge 5$, $8$ when $n=4$, $5$ when $n=3$, $4$ when $n=2$, and $0$ when $n=1$ or $n=0$, which linearly depends on $n$.     

The exponential space of an L2-stochastic process with independent increments

In this note we study the Fock or Exponential space associated to a general L²-stochastic process with independent increments without using multiple Wiener integrals.     

Phase-shift controlling of three solitons in dispersion-decreasing fibers

Nonlinear Dynamics - Phase-shift controlling can attenuate the interactions between solitons and gives practical advantage in optical communication systems. For the variable-coefficient nonlinear...     

Stability relative to a set and to the whole space revisited

In [1] P. Seibert suggested without proof some theorems on stability. These theorems involved two new concepts: The first is a local stability of a subset Y of a metric space X on a subset Z of Y. The second is a notion of conditionally attracting set Y ⊆ X on Z ⊆ Y. Using the first of Seibert's concepts, we suggest new theorems and provide the corresponding proofs. However, our theorems are logically independent of those of Seibert. In addition, a proof of a criterion on local stability suggested by Seibert is given.