Roberto Ku-Carrillo

Autonomous University of Aguascalientes | UAA · Departamento de Matemáticas y Física

Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later reduce it by proposing strategies, there exist a variety of indices, such as the corruption...

We study a full randomization of the complete linear differential equation subject to an infinite train of Dirac's delta functions applied at different time instants. The initial condition and coefficients of the differential equation are assumed to be absolutely continuous random variables, while the external or forcing term is a stochastic proces...

We study, from a probabilistic standpoint, first-order impulsive linear differential equations, where all its parameters (initial condition and coefficients) are absolutely continuous random variables with a joint probability density function. We assume an infinite train of Dirac delta impulse applications at given time instants to control the mode...

An important class of non-homogeneous first-order linear random differential equations subject to an infinite sequence of square impulses with random intensity is studied. In applications, these equations are useful to model the dynamics of a population with periodic harvesting and migration under uncertainties. The solution is explicitly obtained...

We perturbed a family of exponential polynomial maps in order to show both analytically and numerically their unpredictable orbit behavior. Due to the analytical form of the iteration functions the family has numerically different behavior than its correspondent analytical one, which is a topic of paramount importance in computer mathematics. We di...

In this work, we construct simple models in terms of differential equations for the dynamics of pest populations and their management using biological pest control. For the first model used, the effect of the biological control is modelled by a function of repeated infinite impulses. And, our second model uses a periodic function proportional to th...

In the context of mathematical models applied to social sciences, we present and analyze a model based on differential equations for the intimate partner violence (IPV). Such a model describes the dynamics of a heterosexual romantic couple in which the man perpetrates violence against the woman. We focus on incorporating different key factors repor...

Obesity as a risk factor has been found in different types of cancers such as breast cancer and colorectal cancer among others. This challenges us to study the cancer-obesity relationship and the tumor response to chemotherapy. In this work, we study and analyze optimal control protocols for chemotherapy treatments for a mathematical model of cance...

We introduce infinite matrix products including some of their main properties and convergence results. We apply them in order to extend to the matrix scenario the definition of the scalar gamma function given by an infinite product due to Weierstrass. A limit representation of the matrix gamma function is also provided.

Several experimental studies have found that obesity is a risk factor for different types of cancer. In this work we present a mathematical model of cancer tumor growth that takes into account the immune system response and the effects of obesity on the organism with cancer. This model consists of four ordinary differential equations with a logisti...

We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems of ordinary differential equations, where is a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved sol...

In this paper we use analytical tools based in the Painlevé analysis and bifurcation theory to offer stable predator–prey models with age structure. Such models account for within-species and the approach is based at the level of individual organisms. We analyze the type of theoretical predation that a system requires to have real solutions where o...

A general nonlinear age-structured predator–prey model is analyzed to obtain the dynamics of two interacting populations that includes self-limitation on the prey and juvenile predation. Our aim is to identify mechanisms of newborn survival that allow us to explain viable interactions between the two populations in circumstances when their absence...