Traveling front solutions for a diffusive epidemic model with external sources
Triple Collision in the Collinear Three-Body Problem.
Tube-MPC for a class of uncertain continuous nonlinear systems with application to surge problem
This paper presents a new robust adaptive model predictive control for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound, as well as constraints on input states. An adaptive control is used in the new controller to estimate the system uncertainty. Also, to avoid the system disturbances, a method is employed to find the appropriate gain in Tube-MPC. Finally, a surge avoidance problem in centrifugal compressors...
Tumour angiogenesis model with variable vessels' effectiveness
We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties...
Uniform stability of displacement coupled second-order equations.
Uniqueness of limit cycles bounded by two invariant parabolas
In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas.
Universality and scaling in networks of period-doubling maps with a pacemaker.
Using density matrices in classical dynamical systems
Using normal mode analysis in teaching mathematical modeling to biology students
Linear oscillators are used for modeling a diverse array of natural systems, for instance acoustics, materials science, and chemical spectroscopy. In this paper I describe simple models of structural interactions in biological molecules, known as elastic network models, as a useful topic for undergraduate biology instruction in mathematical modeling. These models use coupled linear oscillators to model the fluctuations of molecular structures around the equilibrium state. I present many learning...
Vaccination strategies of population groups with distinct perceived probabilities of infection.
Vacuum energy as spectral geometry.
Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response
The challenges to live in the open water and the diversity of habitats in the marine environments prompts phytoplankton to devise strategies which often involve production of toxins by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor. The functional response of the predator is described by Holling type IV. We investigate wave phenomena and non-linear non-equilibrium pattern formation in a phytoplankton-zooplankton system with Holling type IV functional response....
О геометрии группы диффеоморфизмов и динамике идеальной несжимаемой жидкости
Об однозначной разрешимости задачи Коши для уравнений дискретных киральных полей со значениями в римановых многообразиях
Скрытые симметрии в шестивершинной модели статистической физики
Теория возмущений для основного синглетного состояния гейзенберговской антиферромагнитной цепочки спинов 1/2
Точное решение модели трех связанных осцилляторов с штарковской нелинейностью
Устойчивость отображений гильбертова пространства и эквивалентность управляемых систем