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In this thesis we present a mathematical model describing the population dynamics of molecules in an artificial chemistry where large molecules can be produced by successive ligation of pairs of smaller molecules. The chemistry contains a…

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in…

In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the…

We examine the feasibility of predicting and subsequently managing the future evolution of a Complex Adaptive System. Our archetypal system mimics a competitive population of mechanical, biological, informational or human objects. We show…

The dynamical behavior of two types of non-equilibrium systems is discussed: $(a)$ two-dimensional cellular structures, and $(b)$ living polymers. Simple models governing their evolution are introduced and steady state distributions (cell…

We present a benchmark study of autonomous, chemical agents exhibiting associative learning of an environmental feature. Associative learning has been widely studied in cognitive science and artificial intelligence, but are most commonly…

Standard models of population dynamics focus on the the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the…

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…

Coevolutionary dynamics is investigated in chemical catalysis, biological evolution, social and economic systems. The dynamics of these systems can be analyzed within the unifying framework of evolutionary game theory. In this Letter, we…

Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…

We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…

Understanding how the structure of community interactions is modified by coevolution is vital for understanding system responses to change at all scales. However, in absence of a group selection process, collective community behaviours…

Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…

Compartmentalization of biochemical processes underlies all biological systems, from the organelle to the tissue scale. Theoretical models to study the interplay between noisy reaction dynamics and compartmentalization are sparse, and…

The present study gives a mathematical framework for self-evolution within autonomous problem solving systems. Special attention is set on universal abstraction, thereof generation by net block homomorphism, consequently multiple order…

Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…

Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…

We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in…

A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the…