Related papers: Extreme phase sensitivity in systems with fractal …
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
Topologically ordered phases exhibit further complexity in the presence of global symmetries: Their anyonic excitations may exhibit different transformation patterns under these symmetries, leading to a classification in terms of…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
We show sensitive dependece on initial condition and dense periodic points imply asymptotic sensitivity, a stronger form of sensitivity, where the deviation happens not just once but infintely many times. As a consequence it follows that…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
Among the properties that are common to complex systems, the presence of critical thresholds in the dynamics of the system is one of the most important. Recently, there has been interest in the universalities that occur in the behavior of…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
Assuming a second-order phase transition for the hadronization process, we attempt to associate intermittency patterns in high-energy hadronic collisions to fractal structures in configuration space and corresponding intermittency indices…
Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…
We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing…
An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…
Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of…
Quantum information processing exploits all the features quantum mechanics offers. Among them there is the possibility to induce nonlinear maps on a quantum system by involving two or more identical copies of the given system in the same…
A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories,…
A new type of collective excitations, due exclusively to the topology of a complex random network that can be characterized by a fractal dimension $D_F$, is investigated. We show analytically that these excitations generate phase…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
A wide variety of complex systems exhibit large fluctuations both in space and time that often can be attributed to the presence of some kind of critical phenomena. Under such critical scenario it is well known that the properties of the…
Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…