arXiv subjects

Eva Kaslik

Publications and source records attributed to Eva Kaslik.

24 records · Page 2Linked to original sources

arXiv2016

Stability analysis of a hypothalamic-pituitary-adrenal axis model with inclusion of glucocorticoid receptor and memory

This paper analyzes a four-dimensional model of the hypothalamic-pituitary-adrenal (HPA) axis that includes the influence of the glucocorticoid receptor in the pituitary. Due to the spatial separation between the hypothalamus, pituitary and adrenal glands, distributed time delays are introduced in the mathematical model. The existence of the positive equilibrium point is proved and a local stability and bifurcation analysis is provided, considering several types of delay kernels. The fractional-order model with discrete time delays is also taken into account. Numerical simulations are provided to illustrate the effectiveness of the theoretical findings.

math.OC↗

arXiv2016

A Comparison Between the Stability Properties in a DDE Model for Leukemia and the Modified Fractional Counterpart

In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model takes into account three types of division that a stem-like cell can undergo and cell competition between healthy and leukemia cell populations. The action of the immune system on the leukemic cell populations is also considered. The stability properties of the equilibrium points are established through numerical results and the differences between the two types of approaches are discussed. Medical conclusions are drawn in view of the obtained numerical simulations.

q-bio.PE↗

arXiv2016

Stability and Hopf bifurcation analysis for the hypothalamic-pituitary-adrenal axis model with memory

This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The existence of a unique equilibrium point of the mathematical models is proved and a local stability analysis is undertaken for the system with general distributed delays. A thorough bifurcation analysis for the distributed delay model with several types of delay kernels is provided. Numerical simulations are carried out for the distributed delays models and for the fractional-order model with discrete delays, which substantiate the theoretical findings. It is shown that these models are able to capture the vital mechanisms of the HPA system.

math.DS↗

arXiv2016

Dynamics of complex-valued fractional-order neural networks

The dynamics of complex-valued fractional-order neuronal networks are investigated, focusing on stability, instability and Hopf bifurcations. Sufficient conditions for the asymptotic stability and instability of a steady state of the network are derived, based on the complex system parameters and the fractional order of the system, considering simplified neuronal connectivity structures (hub and ring). In some specific cases, it is possible to identify the critical values of the fractional order for which Hopf bifurcations may occur. Numerical simulations are presented to illustrate the theoretical findings and to investigate the stability of the limit cycles which appear due to Hopf bifurcations.

math.DS↗

arXiv2012

Theoretical Analysis and Tuning of Decentralized Probabilistic Auto-Scaling

A major impediment towards the industrial adoption of decentralized distributed systems comes from the difficulty to theoretically prove that these systems exhibit the required behavior. In this paper, we use probability theory to analyze a decentralized auto-scaling algorithm in which each node probabilistically decides to scale in or out. We prove that, in the context of dynamic workloads, the average load of the system is maintained within a variation interval with a given probability, provided that the number of nodes and the variation interval length are higher than certain bounds. The paper also proposes numerical algorithms for approximating these minimum bounds.

cs.DC↗

arXiv2011

Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions

Using the Mellin transform approach, it is shown that, in contrast with integer-order derivatives, the fractional-order derivative of a periodic function cannot be a function with the same period. The three most widely used definitions of fractional-order derivatives are taken into account, namely, the Caputo, Riemann-Liouville and Grunwald-Letnikov definitions. As a consequence, the non-existence of exact periodic solutions in a wide class of fractional-order dynamical systems is obtained. As an application, it is emphasized that the limit cycle observed in numerical simulations of a simple fractional-order neural network cannot be an exact periodic solution of the system.

math.DS↗