Mathematical and Computational Applications

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observerhttps://www.mdpi.com/2297-8747/25/1/1

Estudio de la dinámica global de modelo de sistemas biológicos que representan concentraciones celulares y su relación con los virus que afectan al sistema inmunológico.

Tesis (Doctorado en ciencias en sistemas digitales), Instituto Politécnico Nacional, SEPI, Citedi, 2016, 1 archivo PDF, (95 pàginas). tesis.ipn.m

On the global dynamics of the cancer AIDS-related mathematical model

summary:In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior

CAR-T Cell Therapy for the Treatment of ALL: Eradication Conditions and In Silico Experimentation

In this paper, we explore the application of Chimeric Antigen Receptor (CAR) T cell therapy for the treatment of Acute Lymphocytic Leukaemia (ALL) by means of in silico experimentation, mathematical modelling through first-order Ordinary Differential Equations and nonlinear systems theory. By combining the latter with systems biology on cancer evolution we were able to establish a sufficient condition on the therapy dose to ensure complete response. The latter is illustrated across multiple numerical simulations when comparing three mathematically formulated administration protocols with one of a phase 1 dose-escalation trial on CAR-T cells for the treatment of ALL on children and young adults. Therefore, both our analytical and in silico results are consistent with real-life scenarios. Finally, our research indicates that tumour cells growth rate and the killing efficacy of the therapy are key factors in the designing of personalised strategies for cancer treatment

ISA Transactions Journal

his paper introduces a novel methodology to detect and identify faults for a class of autonomous nonlinear systems. In the proposed design, a fuzzy extended system observer (FESO) based on the Mandami-type fuzzy system is used to estimate the fault that is considered to be the extended system state. In this method, the Mamdani-type fuzzy system is based on a single-input single-output (SISO) where the observer error is considered as the fuzzy input variable. Additionally, the stability analysis under Lyapunov criteria verifies that the solutions of proposed FESO are ultimately bounded. Finally, simulation examples are given to corroborate the feasibility of the proposed FESO.https://www.sciencedirect.com/science/article/abs/pii/S0019057821005863?via%3Dihu

Bounding the Dynamics of a Chaotic-Cancer Mathematical Model

The complexity of cancer has motivated the development of different approaches to understand the dynamics of this large group of diseases. One that may allow us to better comprehend the behavior of cancer cells, in both short- and long-term, is mathematical modelling through ordinary differential equations. Several ODE mathematical models concerning tumor evolution and immune response have been formulated through the years, but only a few may exhibit chaotic attractors and oscillations such as stable limit cycles and periodic orbits; these dynamics are not that common among cancer systems. In this paper, we apply the Localization of Compact Invariant Sets (LCIS) method and Lyapunov stability theory to investigate the global dynamics and the main factors involved in tumor growth and immune response for a chaotic-cancer system presented by Itik and Banks in 2010. The LCIS method allows us to compute what we define as the localizing domain, which is formulated by the intersection of all lower and upper bounds of each cells population in the nonnegative octant, R+,03. Bounds of this domain are given by inequalities in terms of the system parameters. Then, we apply Lyapunov stability theory and LaSalle’s invariance principle to establish existence conditions of a global attractor. The latter implies that given any nonnegative initial condition, all trajectories will go to the largest compact invariant set (a stable equilibrium point, limit cycles, periodic orbits, or a chaotic attractor) located either inside or at the boundaries of the localizing domain. In order to complement our analysis, numerical simulations are performed throughout the paper to illustrate all mathematical results and to better explain their biological implications

Chaos Synchronization for Hyperchaotic Lorenz-Type System via Fuzzy-Based Sliding-Mode Observer

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer