Browsing by Subject "Complex systems"

Now showing 1 - 3 of 3

Open Access
Analysis of cross-correlations between financial markets after the 2008 crisis
(Elsevier BV, 2013) Sensoy, A.; Yuksel, S.; Erturk, M.
We analyze the cross-correlation matrix C of the index returns of the main financial markets after the 2008 crisis using methods of random matrix theory. We test the eigenvalues of C for universal properties of random matrices and find that the majority of the cross-correlation coefficients arise from randomness. We show that the eigenvector of the largest deviating eigenvalue of C represents a global market itself. We reveal that high volatility of financial markets is observed at the same times with high correlations between them which lowers the risk diversification potential even if one constructs a widely internationally diversified portfolio of stocks. We identify and compare the connection and cluster structure of markets before and after the crisis using minimal spanning and ultrametric hierarchical trees. We find that after the crisis, the co-movement degree of the markets increases. We also highlight the key financial markets of pre and post crisis using main centrality measures and analyze the changes. We repeat the study using rank correlation and compare the differences. Further implications are discussed.
Open Access
Deterministic phase transitions and self-organization in logistic cellular automata
(American Physical Society, 2019) İbrahimi, Muhamet; Gülseren, Oğuz; Jahangirov, Seymur
We present a simple extension in which a single parameter tunes the dynamics of cellular automata (CA) by consequently expanding their discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.
Open Access
Nonlinear and far-from-equilibrium dynamics of optical pulses in fiber oscillators
(2017-08) Teamir, Tesfay Gebremedhin
Fundamentals of mode locking of lasers have been extensively studied and well established for the last three decades. However, it continues to be an intensely studied field. The continued interest is, in part, due to the scientific and technological applications enabled by the generation of ultrashort pulses of light using mode-locking. There is also a deeper reason for the interest. Despite decades of effort, there is still no encompassing theory of mode-locking that applies to the broad range of dynamics displayed by modern mode-locked lasers, in particular, fiber lasers. Mode-locking is a collective phenomenon that arises from the nonlinear interactions between thousands of optical modes supported by a laser cavity, which is typically initiated from laser noise in the cavity. In addition to many unanswered questions from a nonlinear dynamics perspective, there has been limited progress from the point of the thermodynamics, even though mode-locking corresponds to a far-from-equilibrium steady state of a laser. The central premise of this thesis is that mode-locked lasers are invaluable as experimental platforms not only for nonlinear phenomena, but also for far-fromequilibrium dynamics of nonlinear systems, where there is a particular shortage of convenient platforms for experimentation, in addition to the practical interest in development of technically superior lasers. After introductory discussions, we report the direct generation of sub-hundred femtosecond pulses through the interaction of third order dispersion (TOD) and self-phase modulation (SPM) by using two dispersion delay lines (DDLs) inside a laser cavity. Moreover, we report dynamics that are consistent with an effective negative nonlinearity, which is explained through an interplay between self-phase modulation (SPM) and second order dispersion (GVD) for a chirped pulse. Despite numerous studies on their nonlinear dynamics, relatively little is known about the thermodynamics and fluctuations-induced dynamics of mode-locking. We investigate transitions from CW to single pulsing, and then to multipulsing states in the presence of nonlinearity, feedback mechanisms, laser noise (as a source of fluctuations) and the laser’s response to externally injected modulations or fluctuations. Near critical points (instability attractors), dissipative soliton (DS) states are observed to interact between themselves and with their environment which is often followed by random transitions among different pulsing states. This critical behavior appears to be caused by soliton-soliton or solitongenerated dispersive wave interactions in addition to periodic breathing, due to the periodic boundary conditions of the cavity, leading to bifurcations and the onset of chaos. Irrespective of specifics parameters of states, measured noise level (i.e., the strength of fluctuations) of the laser usually starts at a low value, and then slightly reduced as the DSs energy is increased. Further increases in power (nonlinearity) drive it towards a noisy critical state, where random creation or annihilation of pulses occur just before a new steady state is formed. These noiseinduced transitions between steady states far from equilibrium could conceivably shed light on the thermodynamics of other far-from-equilibrium systems. Finally, we demonstrate direct electronic control over mode-locking states using spectral amplitude and phase modulation by incorporating a spatial light modulator (SLM) at a Fourier plane inside the cavity. The modulation enables us to halt and restart mode locking, suppress instabilities, induce controlled reversible and irreversible transitions between mode-locking states, and perform advanced pulse shaping inside a cavity. We also introduce a simple method to manipulate femtosecond optical pulses by directly applying dynamic periodic phase modulation mask on the optical spectrum inside oscillator. With the application of such dynamic periodic linear spectral phase mask we can control the pulse dynamics, demonstrating the capability to tune the pulse-to-pulse separation time, pulse tweezing, blue- and red-shifting of spectral components and pulse splitting. This technique, which is introduced for the first time to our knowledge, may be used in a range of applications such as coherent quantum control, nonlinear spectroscopy, microscopy, in data storage, in the switching of optical and magnetic properties of materials, as well as studies on the fundamentals of oscillator dynamics and other self-organized phenomena in spatiotemporally extended systems.