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Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
In this PhD thesis, I investigate the properties of symmetry-breaking dynamical phase transitions that manifest in the fluctuations of time-integrated observables within classical systems. In particular, I analyze how these phase…
In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit…
We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…
Transient processes in a third-order radiophysical flow system are studied and a map of the transient process duration versus initial conditions is constructed and analyzed. The results are compared to the arrangement of submanifolds of the…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
Multiple stable states - the coexistence of two or more distinct ecological configurations under identical environmental conditions - have attracted sustained interest in ecology, yet the field still lacks a unified framework connecting…
We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and their cycle lengths satisfy a…
The large deviation theory has recently been applied to open quantum systems to uncover dynamical crossovers in the space of quantum trajectories associated to Markovian evolutions. Such dynamical crossovers are characterized by qualitative…
Dynamical phase transitions in the relaxation behavior of stochastic quantum walks are investigated, focusing on systems where coherent unitary evolution is periodically interrupted by dephasing. This interplay leads to a classicalization…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We study the link between relaxation to the equilibrium and anomalous superdiffusive motion in a classical N-body hamiltonian system with long-range interaction showing a second-order phase-transition in the canonical ensemble. Anomalous…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over an arbitrary finite field. For systems that can be…
While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected…
We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found.…
When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence,…
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two matters are considered: the theory of canonical transformations for presymplectic Hamiltonian systems,…
Several nonlinear and nonequilibrium driven as well as active systems (e.g. microswimmers) show bifurcations from one state to another (for example a transition from a non motile to motile state for microswimmers) when some control…