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distribution consistent with the characteristics of rare events. The interevent intervals obey a
Poisson-like distribution. We have located the parameter regions of extreme events in phase
diagrams. Furthermore, we have studied two Ikeda maps to explore how and when extreme
events terminate via mutual interaction. A pure diffusion of information exchange is unable to
terminate extreme events where synchronous occurrence of extreme events is only possible
even for large interaction. On the other hand, a threshold-activated coupling can terminate
extreme events above a critical value of mutual interaction.

Next, we have proposed a minimal model of moving agents where the network of contacts
changes over time due to their motion. In particular, agents interact based on their proximity in
a two-dimensional space, but only if they belong to the same fixed interaction zones. Our
research reveals the emergence of global synchronization if all the interaction zones are
attractive. However, if some of the interaction zones are repulsive, they deflect synchrony and
lead to short-lasting but recurrent deviations that constitute extreme events in the network. We
have used two paradigmatic oscillators for the description of the agent dynamics to demonstrate
our findings numerically, and we also provided an analytical formulation to describe the
emergence of complete synchrony and the thresholds that distinguish extreme events from
other intermittent states based on the peak-over-threshold approach.

Now, we are interested to investigate the El-Nino-Southern Oscillation phenomenon in a
nonlinear low dimensional model and try to understand the dynamic origin of the extreme El-
Nino events, which is elusive still now.

Related papers:

1. Arnob Ray, Sarbendu Rakshit, Dibakar Ghosh and Syamal K. Dana “Intermittent
large deviation of chaotic trajectory in Ikeda map: Signature of extreme events",
CHAOS, 29, 043131 (2019).
2. Sayantan Nag Chowdhury, Soumen Majhi, Mahmut Ozer, Dibakar Ghosh and
Matjaz Perc, "Synchronization to extreme events in moving agents", New Journal of
Physics, 21, 073048, 2019.
3. Arnob Ray, Sarbendu Rakshit, Gopal K. Basak, Syamal K. Dana and Dibakar
Ghosh, "Understanding the origin of extreme events in El-Nino southern oscillation",
Physical Review E, 101, 062210, 2020.
4. Ray, A Mishra, Dibakar Ghosh, T Kapitaniak, SK Dana, C Hens, “Extreme events in
a network of heterogeneous Josephson junctions”, Physical Review E 101 (3),
032209, 2020.

Synchronization in temporal dynamical networks:

Recent researches attest to the fact that synchronization in time-varying complex network is
very essential due to its possible applications in various fields. Particularly, in-fields like
mobile communications, robotics etc. Synchrony among moving and dynamic agents is
certainly necessary. For some situations in coordinated motions of vehicles, flashing fireflies
and swarming bird’s etc. interaction with any other agent lying in a specified zone may not
always be possible. We tried to resolve this issue by forming those zones in a slightly different
manner and examine global synchrony in a network of mobile agents moving in a finite arena
of three-dimensional spaces, where an oscillator is assigned for each agent. In this context, both
limit cycle and chaotic systems have been dealt with. The interaction between the oscillators
depends on their proximity and the orientation of the movements as well. We elaborately

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