Showing papers by "Stefano Boccaletti published in 2022"

Topological synchronization of chaotic systems

Abstract: A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature. Classically, synchronization was characterized in terms of macroscopic parameters, such as the spectrum of Lyapunov exponents. Recently, however, we attempted a microscopic description of synchronization, called topological synchronization, and showed that chaotic synchronization is, in fact, a continuous process that starts in low-density areas of the attractor. Here we analyze the relation between the two emergent phenomena by shifting the descriptive level of topological synchronization to account for the multifractal nature of the visited attractors. Namely, we measure the generalized dimension of the system and monitor how it changes while increasing the coupling strength. We show that during the gradual process of topological adjustment in phase space, the multifractal structures of each strange attractor of the two coupled oscillators continuously converge, taking a similar form, until complete topological synchronization ensues. According to our results, chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what we termed as the 'zipper effect', a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. Topological synchronization offers, therefore, a more detailed microscopic description of chaotic synchronization and reveals new information about the process even in cases of high mismatch parameters.

Implementing and morphing Boolean gates with adaptive synchronization: The case of spiking neurons

Abstract: Boolean logic is the paradigm through which modern computation is performed in silica. When nonlinear dynamical systems are interacting in a directed graph, we show that computation abilities emerge spontaneously from adaptive synchronization, which actually can emulate Boolean logic. Precisely, we demonstrate that a single dynamical unit, a spiking neuron modeled by the Hodgkin-Huxley model, can be used as the basic computational unit for realizing all the 16 Boolean logical gates with two inputs and one output, when it is coupled adaptively in a way that depends on the synchronization level between the two input signals. This is realized by means of a set of parameters, whose tuning offers even the possibility of constructing a morphing gate, i.e., a logical gate able to switch efficiently from one to another of such 16 Boolean gates. Extensive simulations demonstrate the efficiency and the accuracy of the proposed computational paradigm.

A compartmental model for cyber-epidemics

Abstract: In our more and more interconnected world, a specific risk is that of a cyber-epidemic (or cyber-pandemic), produced either accidentally or intentionally, where a cyber virus propagates from device to device up to undermining the global Internet system with devastating consequences in terms of economic costs and societal harms related to the shutdown of essential services. We introduce a compartmental model for studying the spreading of a malware and of the awareness of its incidence through different waves which are evolving on top of the same graph structure (the global network of connected devices). This is realized by considering vectorial compartments made of two components, the first being descriptive of the state of the device with respect to the new malware's propagation, and the second accounting for the awareness of the device's user about the presence of the cyber threat. By introducing suitable transition rates between such compartments, one can then follow the evolution of a cyber-epidemic from the moment at which a new virus is seeded in the network, up to when a given user realizes that his/her device has suffered a damage and consequently starts a wave of awareness which eventually ends up with the development of a proper antivirus software. We then compare the overall damage that a malware is able to produce in Erd\H{o}s-R\'enyi and scale-free network architectures for both the case in which the virus is causing a fixed damage on each device and the case where, instead, the virus is engineered to mutate while replicating from device to device. Our result constitute actually the attempt to build a specific compartmental model whose variables and parameters are entirely customized for describing cyber-epidemics.

Mean-field nature of synchronization stability in networks with multiple interaction layers

Abstract: Abstract The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.

Mean-field nature of synchronization stability in networks with multiple interaction layers

Abstract: Abstract The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.

Why are there six degrees of separation in a social network?

Abstract: A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most social networks are organized so that no individual is more than six connections apart from any other, an empirical regularity known as the six degrees of separation. Why social networks have this ultra-small world organization, whereby the graph's diameter is independent of the network size over several orders of magnitude, is still unknown. We show that the 'six degrees of separation' are the property featured by the equilibrium state of any network where individuals weigh between their aspiration to improve their centrality and the costs incurred in forming and maintaining connections. We show, moreover, that the emergence of such a regularity is compatible with all other features, such as clustering and scale-freeness, that normally characterize the structure of social networks. Thus, our results show how simple evolutionary rules of the kind traditionally associated with human cooperation and altruism can also account for the emergence of one of the most intriguing attributes of social networks.