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The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics.…
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…
The dynamics of an extended, spatiotemporally chaotic system might appear extremely complex. Nevertheless, the local dynamics, observed through a finite spatiotemporal window, can often be thought of as a visitation sequence of a finite…
Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results…
We present a comprehensive study for the statistical properties of random variables that describe the domain structure of a finite Ising chain with nearest-neighbor exchange interactions and free boundary conditions. By use of extensive…
Each connected component of a mapping $\{1,2,...,n\}\rightarrow\{1,2,...,n\}$ contains a unique cycle. The largest such component can be studied probabilistically via either a delay differential equation or an inverse Laplace transform. The…
We present a detailed algorithm to construct symbolic encodings for chaotic attractors of three-dimensional flows. It is based on a topological analysis of unstable periodic orbits embedded in the attractor and follows the approach proposed…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
Log-periodic amplitudes of the surface magnetization are calculated analytically for two Ising quantum chains with aperiodic modulations of the couplings. The oscillating behaviour is linked to the discrete scale invariance of the…
Period mappings were introduced in the sixties [G] to study variation of complex structures of families of algebraic varieties. The theory of tautological systems was introduced recently [LSY,LY] to understand period integrals of algebraic…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
The fields of time series and graphical models emerged and advanced separately. Previous work on the structure learning of continuous and real-valued time series utilizes the time domain, with a focus on either structural autoregressive…
One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are…
Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…
Schematic maps are in daily use to show the connectivity of subway systems and to facilitate travellers to plan their journeys effectively. This study surveys up-to-date algorithmic approaches in order to give an overview of the state of…
Deterministic routing has emerged as a promising technology for future non-terrestrial networks (NTNs), offering the potential to enhance service performance and optimize resource utilization. However, the dynamic nature of network topology…
Networks are used as highly expressive tools in different disciplines. In recent years, the analysis and mining of temporal networks have attracted substantial attention. Frequent pattern mining is considered an essential task in the…
Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique…