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Register a new userResilience of networks of multi-stable chaotic systems to targetted attacks
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We investigate the collective dynamics of chaotic multi-stable Duffing oscillators connected in different network topologies, ranging from star and ring networks, to scale-free networks. We estimate the resilience of such networks by introducing a variant of the concept of multi-node Basin Stability, which allows us to gauge the global stability of the collective dynamics of the network in response to large perturbations localized on certain nodes. We observe that in a star network, perturbing just the hub node has the capacity to destroy the collective state of the entire system. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state. This demonstrates the drastic effect of the centrality of the perturbed node on the collective dynamics of the full network. Further, we explore scale-free networks of such multi-stable oscillators and demonstrate that targetted attacks on nodes with high centrality can destroy the collective dynamics much more efficiently than random attacks, irrespective of the nature of the nodal dynamics and type of perturbation. We also find clear evidence that the betweeness centrality of the perturbed node is most crucial for dynamical robustness, with the entire system being more vulnerable to attacks on nodes with high betweeness. These results are crucial for deciding which nodes to stringently safeguard in order to ensure the recovery of the network after targetted localized attacks.
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We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the mean-field of the oscillators below it in the hierarchy, and couples diffusively to the oscillator above it in the hierarchy. We find that coupling to one dissimilar external system manages to suppress the chaotic dynamics of all the oscillators in the network at sufficiently high coupling strength. This holds true irrespective of whether the connection to the external system is direct or indirect through oscillators at another level in the hierarchy. Investigating the synchronization properties show that the oscillators have the same steady state at a particular level of hierarchy, whereas the steady state varies across different hierarchical levels. We quantify the efficacy of control by estimating the fraction of random initial states that go to fixed points, a measure analogous to basin stability. These quantitative results indicate the easy controllability of hierarchical networks of chaotic oscillators by an external chaotic system, thereby suggesting a potent method that may help design control strategies.
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some recently developed techniques for the spectral form factor of systems with hyperbolic and ergodic underlying classical dynamics and f=2 degrees of freedom, that allow us to go beyond the diagonal approximation. First we extend these techniques to systems with f>2. Then we use these results to calculate the generalized form factor. We show that the dependence on the rescaled time in units of the Heisenberg time is universal for both the spectral and the generalized form factor. Furthermore, we derive a relation between the generalized form factor and the classical time-correlation function of the Weyl symbols of the quantum operators.
We study the synchronization of chaotic units connected through time-delayed fluctuating interactions. We focus on small-world networks of Bernoulli and Logistic units with a fixed chiral backbone. Comparing the synchronization properties of static and fluctuating networks, we find that random network alternations can enhance the synchronizability. Synchronized states appear to be maximally stable when fluctuations are much faster than the time-delay, even when the instantaneous state of the network does not allow synchronization. This enhancing effect disappears for very slow fluctuations. For fluctuation time scales of the order of the time-delay, a desynchronizing resonance is reported. Moreover, we observe characteristic oscillations, with a periodicity related to the coupling delay, as the system approaches or drifts away from the synchronized state.
The resilience of cyberphysical systems to denial-of-service (DoS) and integrity attacks is studied in this paper. The cyberphysical system is modeled as a linear structured system, and its resilience to an attack is interpreted in a graph theoretical framework. The structural resilience of the system is characterized in terms of unmatched vertices in maximum matchings of the bipartite graph and connected components of directed graph representations of the system under attack. We first present conditions for the system to be resilient to DoS attacks when an adversary may block access or turn off certain inputs to the system. We extend this analysis to characterize resilience of the system when an adversary might additionally have the ability to affect the implementation of state-feedback control strategies. This is termed an integrity attack. We establish conditions under which a system that is structurally resilient to a DoS attack will also be resilient to a certain class of integrity attacks. Finally, we formulate an extension to the case of switched linear systems, and derive conditions for such systems to be structurally resilient to a DoS attack.
We investigate the collective dynamics of bi-stable elements connected in different network topologies, ranging from rings and small-world networks, to scale-free networks and stars. We estimate the dynamical robustness of such networks by introducing a variant of the concept of multi-node basin stability, which allows us to gauge the global stability of the dynamics of the network in response to local perturbations affecting a certain class of nodes of a system. We show that perturbing nodes with high closeness and betweeness-centrality significantly reduces the capacity of the system to return to the desired state. This effect is very pronounced for a star network which has one hub node with significantly different closeness/betweeness-centrality than all the peripheral nodes. In such a network, perturbation of the single hub node has the capacity to destroy the collective state. On the other hand, even when a majority of the peripheral nodes are strongly perturbed, the hub manages to restore the system to its original state, demonstrating the drastic effect of the centrality of the perturbed node on the dynamics of the network. Further, we explore explore Random Scale-Free Networks of bi-stable dynamical elements. We exploit the difference in the distribution of betweeness centralities, closeness centralities and degrees of the nodes in Random Scale-Free Networks with m=1 and m=2, to probe which centrality property most influences the robustness of the collective dynamics in these heterogeneous networks. Significantly, we find clear evidence that the betweeness centrality of the perturbed node is more crucial for dynamical robustness, than closeness centrality or degree of the node. This result is important in deciding which nodes to safeguard in order to maintain the collective state of this network against targeted localized attacks.
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