Complex Systems
Current Issue

Volume 30, Number 1 (2021)

Tools to Characterize the Correlated Nature of Collective Dynamics Download PDF
R. Vilela Mendes and Carlos Aguirre

Synchronization, which occurs for both chaotic and nonchaotic systems, is a striking phenomenon with many practical implications for natural phenomena and technological applications. However, even before synchronization, strong correlations and complex patterns occur in the collective dynamics of natural systems. To characterize their nature is essential for understanding many phenomena in physical and social sciences as well as the perspectives to control their behavior. Because simple correlation measures are unable to characterize these collective patterns, we have developed more general methods for their detection and parametrization. The emergence of patterns of strong correlations before synchronization is illustrated in a few models. They are shown to be associated with the behavior of ergodic parameters. The models are then used as a testing ground of the new pattern characterization tools.

Keywords: correlation; synchronization; chaotic dynamics; complex patterns  

Cite this publication as:
R. Vilela Mendes and C. Aguirre, “Tools to Characterize the Correlated Nature of Collective Dynamics,” Complex Systems, 30(1), 2021 pp. 1–32.

Causal Paths in Temporal Networks of Face-to-Face Human Interactions Download PDF
Agostino Funel

In a temporal network, causal paths are characterized by the fact that links from a source to a target must respect the chronological order. In this paper we study the causal paths structure in temporal networks of face-to-face human interactions in different social contexts. In a static network, paths are transitive; that is, the existence of a link from a to b and from b to c implies the existence of a path from a to c via b. In a temporal network, the chronological constraint introduces time correlations that affect transitivity. A probabilistic model based on higher-order Markov chains shows that correlations that can invalidate transitivity are present only when the time gap between consecutive events is larger than the average value and are negligible below such a value. The comparison between the densities of the temporal and static accessibility matrices shows that the static representation can be used with good approximation. Moreover, we quantify the extent of the causally connected region of the networks over time.

Keywords: temporal networks; human interactions; causal paths; Markov chains; probabilistic models

Cite this publication as:
A. Funel, “Causal Paths in Temporal Networks of Face-to-Face Human Interactions,” Complex Systems, 30(1), 2021 pp. 33–46.

Application of Coupled Map Lattice as an Alternative to Classical Finite Difference Method for Solving the Convection-Diffusion Boundary Value Problem Download PDF
Lukasz Korus

This paper presents a mathematical model for a piston flow reactor based on the material balance law using partial differential equations. A more general, nondimensional variant of the model is also derived. The finite difference method and coupled map lattice are used to create numerical algorithms to simulate spatio-temporal behavior in the studied system. The paper also includes a stability analysis of the proposed algorithms and results of numerous numerical simulations, done in order to compare both methods and to visualize the spatio-temporal behavior of the reactor and the effects of different model parameters. Discussion of the obtained results and comparison of both algorithms is also provided.

Keywords: piston flow reactor; plug flow reactor; distributed parameter systems; coupled map lattice

Cite this publication as:
L. Korus, “Application of Coupled Map Lattice as an Alternative to Classical Finite Difference Method for Solving the Convection-Diffusion Boundary Value Problem,” Complex Systems, 30(1), 2021 pp. 47–73.

Evolutions of Some One-Dimensional Homogeneous Cellular Automata Download PDF
Sreeya Ghosh

Evolution patterns of a one-dimensional homogeneous cellular automaton (CA) are investigated for some standard transition functions. The different possible evolution patterns for an elementary CA starting with at most one active cell or ON state cell are discussed. Also, with respect to some initial configurations, evolution-wise equivalent Wolfram codes are investigated. It is shown that these equivalent codes are automorphic.

Keywords: cellular automaton; evolution pattern; evolution-wise equivalent Wolfram code; elementary cellular automaton

Cite this publication as:
S. Ghosh, “Evolutions of Some One-Dimensional Homogeneous Cellular Automata,” Complex Systems, 30(1), 2021 pp. 75–92.

Classification of Chaotic Behaviors in Jerky Dynamical Systems Download PDF
Tianyi Wang

Differential equations are widely used to model systems that change over time, some of which exhibit chaotic behaviors. This paper proposes two new methods to classify these behaviors that are utilized by a supervised machine learning algorithm. Dissipative chaotic systems, in contrast to conservative chaotic systems, seem to follow a certain visual pattern. Also, the machine learning program written in the Wolfram Language is utilized to classify chaotic behavior with an accuracy around 99.1±1.1%.

Keywords: chaotic systems; jerky dynamics; differential equations; dynamical systems; phase space; supervised machine learning

Cite this publication as:
T. Wang, “Classification of Chaotic Behaviors in Jerky Dynamical Systems,” Complex Systems, 30(1), 2021 pp. 93–110.

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