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Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
We study the quantum mechanics of a billiard (Robnik 1983) in the regime of mixed-type classical phase space (the shape parameter \lambda=0.15) at very high-lying eigenstates, starting at about 1.000.000th eigenstate and including the…
We show that the dynamics of simple disordered models, like the directed Trap Model and the Random Energy Model, takes place at a coexistence point between active and inactive dynamical phases. We relate the presence of a dynamic phase…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
The statistics of Poincar\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this…
It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same…
Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
We study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks, scale free networks, small world networks, tree networks, and random networks. For small coupling strengths nodes show…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
While multiple time scales generally arise in the dynamics of disordered systems, we find multiple time scales in absence of disorder, in a simple model with hard local constraints. The dynamics of the model, which consists of local…
The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization…
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the L\'evy flights in two dimensions (2D). The efficacy of our proposed model is…
In this paper, we report the enhanced stability of induced synchronization by transient uncoupling observed in certain unidirectionally coupled second-order chaotic systems. The stability of synchronization observed in the coupled systems…