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Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under…
We study the discrete-time dynamical systems associated to a stage-structured wild and sterile mosquito population. We describe all fixed points of the evolution operator (which depends on five parameters) of mosquito population and show…
Fundamental properties of macroscopic gene-mating dynamic evolutionary systems are investigated. We focus on a single locus, any number of alleles in a two-gender dioecious population, for a large class of systems within population…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
The concentration gradient of the Bicoid morphogen, which is established during the early stages of a Drosophila melanogaster embryonic development, determines the differential spatial patterns of gene expression and subsequent cell fate…
We explore the bifurcations and dynamics of a scalar differential equation with a single constant delay which models the population of human hematopoietic stem cells in the bone marrow. One parameter continuation reveals that with a delay…
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a…
In dynamical systems theory, a fixed point of the dynamics is called nonhyperbolic if the linearization of the system around the fixed point has at least one eigenvalue with zero real part. The center manifold existence theorem guarantees…
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
Genes are connected in complex networks of interactions where often the product of one gene is a transcription factor that alters the expression of another. Many of these networks are based on a few fundamental motifs leading to switches…
Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure.…
Cellular behavior is governed by gene regulatory processes that are intrinsically dynamic and nonlinear, and are subject to non-negligible amounts of random fluctuations. Such conditions are ubiquitous in physical systems, where they have…
Organismal phenotypes emerge from a complex set of genotypic interactions. While technological advances in sequencing provide a quantitative description of an organism's genotype, characterization of an organism's physical phenotype lags…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
Despite the advent of several novel, synthetic gene drive mechanisms and their potential to one-day control a number of devastating diseases, among other applications, practical use of these systems remains contentious and risky. In…