Overcoming network resilience to synchronization through non-fast stochastic broadcasting

Russell Jeter, Maurizio Porfiri, Igor Belykh
2018 Chaos  
Stochastic broadcasting is an important and understudied paradigm for controlling networks. In this paper, we examine the feasibility of on-off broadcasting from a single reference node to induce synchronization in a target network with connections from the reference node that stochastically switch in time with an arbitrary switching period. Internal connections within the target network are static and promote the network's resilience to externally induced synchronization. Through rigorous
more » ... matical analysis, we uncover a complex interplay between the network topology and the switching period of stochastic broadcasting, fostering or hindering synchronization to the reference node. We derive a criterion which reveals an explicit dependence of induced synchronization on the properties of the network (the Laplacian spectrum) and the switching process (strength of broadcasting, switching period, and switching probabilities). With coupled chaotic tent maps as our test-bed, we prove the emergence of "windows of opportunity" where only non-fast switching periods are favorable to synchronization. The size of these windows of opportunity is shaped by the Laplacian spectrum such that the switching period needs to be manipulated accordingly to induce synchronization. Surprisingly, only the zero and the largest eigenvalues of the Laplacian matrix control these windows of opportunities for tent maps within a wide parameter region. Published by AIP Publishing. https:// Broadcasting propaganda is a manipulative approach used to promote a particular political cause or influence public opinion. Similarly to this abused art of persuasion, driving a technological or biological network towards some desired behavior via global broadcasting from an external node is an effective tool for controlling networks. Examples include a robotic leader influencing the behavior of a school of fish, or a small group of neurons which can form an epileptic focus and cause an epileptic seizure. In this paper, we study the conditions under which a reference broadcasting node can synchronize a target network by stochastically transmitting sporadic, possibly conflicting signals. We demonstrate that manipulating the rate at which the connections between the broadcasting node and the network stochastically switch can overcome network resilience to synchronization. Through a rigorous mathematical treatment, we discover a nontrivial interplay between the network properties that control this resilience and the switching rate of stochastic broadcasting that should be adapted to induce synchronization. Unexpectedly, non-fast switching rates controlling the so-called windows of opportunity guarantee stable synchrony, whereas fast or slow switching leads to desynchronization, even though the networked system spends more time in a state favorable to synchronization.
doi:10.1063/1.5044420 pmid:30070517 fatcat:r32nznbajrfibdeqx6lrofurmm