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In this paper we present a study of local dynamics of the growth of cancer tumor and healthy cells considering the presence of nutrients in the system. We also analyze the evolution of system if we take indirectly into account the level of…
The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative…
The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the…
The recurrence-based divergence quantifier ($DIV$), traditionally applied to dissipative systems, is shown here to be an effective finite-time chaos indicator for conservative dynamics. We benchmark its performances against the…
In this study, we develop consistent estimators for key parameters that govern the dynamics of tumor cell populations when subjected to pharmacological treatments. While these treatments often lead to an initial reduction in the abundance…
This paper is devoted to the solution and stability of a one-dimensional model depicting Rao--Nakra sandwich beams, incorporating damping terms characterized by fractional derivative types within the domain, specifically a generalized…
In this paper, we study a system of three evolutionary operator equations involving fractional powers of selfadjoint, monotone, unbounded, linear operators having compact resolvents. This system constitutes a generalized and relaxed version…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
In this paper the dynamics of a fractional order system modelling the interaction between dark matter and dark energy is analytically and numerically studied. It is shown for the first time that systems modelling the interaction between…
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
The goal of this paper is to establish a general framework for dynamic behaviors of coupled fractional-order stochastic dynamic systems of particles by using star-coupled models. In particular, the general mechanics on the dynamic behaviors…
Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often…
In the framework of a recently developed theory for Hamiltonian chaos, which makes use of the formulation of Newtonian dynamics in terms of Riemannian differential geometry, we obtained analytic values of the largest Lyapunov exponent for…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
We study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy $R$ and the squared frequency ratio $\mu$. By randomly sampling the isoenergetic volume to…
We study systems with periodically oscillating parameters that can give way to complex periodic or non periodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…