On a Mathematical Model of a General Autoimmune Disease

Kolev, Mikhail; Netov, Nikolay; Nikolova, Iveta; Naskinova, Irina; Kuneva, Velika; Milev, Marian

doi:10.3390/axioms12111021

Cited by 2 publications

(1 citation statement)

References 35 publications

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“…It does not only remember the amount of charge flowing through it but it also changes the resistance by controlling the current flowing through it, which is physically realizable and is considered to have the potential to subvert the traditional mode and trigger a circuit revolution. It has garnered attention in various fields including computer science [4,5], neural networks [6,7], telecommunications engineering [8,9], biological engineering [10,11] and other disciplines.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Liu,

Tian,

Wang

et al. 2023

Axioms

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In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.

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Section: Introductionmentioning

confidence: 99%

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Liu,

Tian,

Wang

et al. 2023

Axioms

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Thermostatted Kinetic Theory Structures in Biophysics: Generalizations and Perspectives

Bianca

2024

AppliedMath

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The mathematical modeling of multicellular systems is an important branch of biophysics, which focuses on how the system properties emerge from the elementary interaction between the constituent elements. Recently, mathematical structures have been proposed within the thermostatted kinetic theory for the modeling of complex living systems and have been profitably employed for the modeling of various complex biological systems at the cellular scale. This paper deals with a class of generalized thermostatted kinetic theory frameworks that can stand in as background paradigms for the derivation of specific models in biophysics. Specifically, the fundamental homogeneous thermostatted kinetic theory structures of the recent literature are recovered and generalized in order to take into consideration further phenomena in biology. The generalizations concern the conservative, the nonconservative, and the mutative interactions between the inner system and the outer environment. In order to sustain the strength of the new structures, some specific models of the literature are reset into the style of the new frameworks of the thermostatted kinetic theory. The selected models deal with breast cancer, genetic mutations, immune system response, and skin fibrosis. Future research directions from the theoretical and modeling viewpoints are discussed in the whole paper and are mainly devoted to the well-posedness in the Hadamard sense of the related initial boundary value problems, to the spatial–velocity dynamics and to the derivation of macroscopic-scale dynamics.

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On a Mathematical Model of a General Autoimmune Disease

Cited by 2 publications

References 35 publications

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System

Thermostatted Kinetic Theory Structures in Biophysics: Generalizations and Perspectives

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