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Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
There is a growing body of work considering the use of representations based upon genetic regulatory networks. This paper uses a recently presented abstract, tunable Boolean regulatory network model to explore aspects of mobile DNA, such as…
This paper investigates the evolution of a multi-locus biological system. The evolution of such a system is described by a quadratic stochastic operator (QSO) defined on a simplex. We demonstrate that this QSO can be decomposed into an…
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
This paper describes the optimal selection of a control policy to program the steady state of controlled nonlinear systems with hyperbolic fixed points. This work is motivated by the field of synthetic biology, in which saddle points are…
Gene regulation is an important fundamental biological process. The regulation of gene expression is managed through a variety of methods including epigenetic processes (e.g., DNA methylation). Understanding the role of epigenetic changes…
Drosophila melanogaster, a small dipteran of African origin, represents one of the best-studied model organisms. Early work in this system has uniquely shed light on the basic principles of genetics and resulted in a versatile collection of…
Complex systems with tightly coadapted parts frequently appear in living systems and are difficult to account for through Darwinian evolution, that is random variation and natural selection, if the constituent parts are independently coded…
Computer simulations are an important tool for studying the mechanics of biological evolution. In particular, in silico work with agent-based models provides an opportunity to collect high-quality records of ancestry relationships among…
We consider a Stokes flow coupled with advective-diffusive transport in an evolving domain with boundary conditions allowing for inflow and outflow. The evolution of the domain is induced by the transport process, leading to a fully coupled…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
The development of multicellular organisms entails a deep connection between time-dependent biochemical processes taking place at the subcellular level, and the resulting macroscopic phenotypes that arise in populations of up to trillions…
Evolutionary game dynamics describes the spreading of successful strategies in a population of reproducing individuals. Typically, the microscopic definition of strategy spreading is stochastic, such that the dynamics becomes deterministic…
We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-markovian telegraphic signal…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
We consider a discrete-time dynamical system generated by a nonlinear operator (with four real parameters $a,b,c,d$) of ocean ecosystem. We find conditions on the parameters under which the operator is reduced to a $\ell$-Volterra quadratic…