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Dynamics of a Piecewise-Linear Morris–Lecar Model: Bifurcations and Spike Adding
Multiple-timescale systems often display intricate dynamics, yet of great mathematical interest and well suited to model real-world phenomena such as...
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Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model
In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor (PS) doubly-curved shell resting on the Pasternak foundation...
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Discontinuous Map**s and the Limit Load in Boundary Value Problems of Nonlinear Elasticity
AbstractThe paper considers a boundary-value problem of nonlinear elasticity for a map** (deformation) in two weak formulations: in the form of a...
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Mathematical Foundation of Fractional Calculus
In the long history of the development of fractional calculus, a variety of definitions have been proposed by researchers from different...
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Noise-induced transitions in an avian influenza model with the Allee effect
This paper presents noise-induced transitions in a stochastic avian influenza model with Allee effect. In the deterministic case, one of three...
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A Note on the Stationary Probability Density Function and Covariance Matrix of a Stochastic Chemostat Model with Distributed Delay
In this paper, we will focus on the stochastic chemostat model with distributed delay and Monod-type nutrient absorption function in Stratonovich...
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A Time-Dependent SIRD Nonlinear Cross-Diffusion Epidemic Model: Multiscale Derivation and Computational Analysis
A time-dependent Susceptible-Infected-Recovered-Dead nonlinear cross-diffusion epidemic model is proposed in this chapter. This macro-scale model is...
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The Spectrum and Lyapunov Linear Instability of the Stationary State for Polymer Fluid Flows:The Vinogradov–Pokrovskii Model
We study the Lyapunov linear stability of the stationary state for flows of an incompressible viscoelastic polymer fluid in an infinite planar...
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Husserlian Pure Logic from the Standpoint of Intentionality
This chapter is about Husserl’s idea of pure logic as it is coined in the Logical Investigations. It confronts this idea against the...
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A kinetic model of polyatomic gas with resonant collisions
We propose a kinetic model describing a polyatomic gas undergoing resonant collisions, in which the microscopic internal and kinetic energies are...
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Quasi-Stability of Coexisting Attractors of a Neurodynamic Model with Delay
The problem of the coexistence of quasi-stable attractors of a neurodynamic model with delay is considered. The model is a system of two specially...
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A stochastic hierarchical model for low grade glioma evolution
A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using a piecewise...
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A Model for Craquelure: Brittle Layers on Elastic Substrates
We propose a model for a brittle layer of material on an elastic substrate, with in mind a layer of paint on canvas. The deformation of the...
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Idealized multiple-timescale model of cortical spreading depolarization initiation and pre-epileptic hyperexcitability caused by NaV1.1/SCN1A mutations
Na V 1.1 ( SCN1A ) is a voltage-gated sodium channel mainly expressed in GABAergic neurons. Loss of function mutations of Na V 1.1 lead to epileptic...
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Rheological Vinogradov-Pokrovski Model. Lyapunov Linear Instability of the Stationary Flows of Polymeric Fluid in an Infinite Plane Channel with Perforated Walls
We study a rheological Vinogradov-Pokrovski model for the flows of solutions and melts of incompressible viscoelastic polymeric medium in case of a...
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A Multigenerational Turing Model Reproduces Transgressive Petal Spot Phenotypes in Hybrid Mimulus
The origin of phenotypic novelty is a perennial question of genetics and evolution. To date, few studies of biological pattern formation specifically...
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Peirce and Grothendieck on Mathematical Cognition: A Merging of the Pragmaticist Maxim and Topos Theory
Around the problematics of “mathematical cognition,” some Peircean and Grothendieckean tools are presented (Pragmaticist Maxim and Topos Theory),...
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Active Force Generation in Cardiac Muscle Cells: Mathematical Modeling and Numerical Simulation of the Actin-Myosin Interaction
Cardiac in silico numerical simulations are based on mathematical models describing the physical processes involved in the heart function. In this...
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Minimal Morphoelastic Models of Solid Tumour Spheroids: A Tutorial
Tumour spheroids have been the focus of a variety of mathematical models, ranging from Greenspan’s classical study of the 1970 s through to...
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