title: Local instability driving extreme events in a pair of coupled chaotic electronic circuits.
abstract: For a long time, extreme events happening in complex systems, such as financial markets, earthquakes, and neurological networks, were thought to follow power-law size distributions. More recently, evidence suggests that in many systems the largest and rarest events differ from the other ones. They are dragon kings, outliers that make the distribution deviate from a power law in the tail. Understanding the processes of formation of extreme events and what circumstances lead to dragon kings or to a power-law distribution is an open question and it is a very important one to assess whether extreme events will occur too often in a specific system. In the particular system studied in this paper, we show that the rate of occurrence of dragon kings is controlled by the value of a parameter. The system under study here is composed of two nearly identical chaotic oscillators which fail to remain in a permanently synchronized state when coupled. We analyze the statistics of the desynchronization events in this specific example of two coupled chaotic electronic circuits and find that modifying a parameter associated to the local instability responsible for the loss of synchronization reduces the occurrence of dragon kings, while preserving the power-law distribution of small- to intermediate-size events with the same scaling exponent. Our results support the hypothesis that the dragon kings are caused by local instabilities in the phase space.
authors.affiliation: Departamento de Física/CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.
authors.forename: Gilson F
authors.initials: GF
authors.lastname: de Oliveira
authors.affiliation: Departamento de Física/CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.
authors.forename: Orlando
authors.initials: O
authors.lastname: Di Lorenzo
authors.affiliation: Departamento de Física/CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.
authors.forename: Thierry Passerat
authors.initials: TP
authors.lastname: de Silans
authors.affiliation: Departamento de Física/CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.
authors.forename: Martine
authors.initials: M
authors.lastname: Chevrollier
authors.affiliation: Departamento de Física/CCEN, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.
authors.forename: Marcos
authors.initials: M
authors.lastname: Oriá
authors.affiliation: Departamento de Informática, Centro de Informática, Universidade Federal da Paraíba, Av. dos Escoteiros s/n, Mangabeira VII, 58055-000, João Pessoa-PB, Brazil.
authors.forename: Hugo L D de Souza
authors.initials: HL
authors.lastname: Cavalcante