#### Hall 123

#### Emergent Dynamics of Slow and Fast Systems on Complex Networks

#### Kajari Gupta

##### Indian Institute of Science Education and Research (IISER) Pune

*In the real world, we see physical, biological , geophysical systems that are consist of large number of interacting dynamical entities to form a complex structure. In this context the study of emergent dynamics of individual systems are largely studied and had been applied to its contribution towards control of chaos, self organization, synchronization etc. In many such cases the dynamics of individual entities follow different time scale for their evolution in time. In our work we consider standard non linear systems with differing time scales interacting with each other. We start by taking the simplest case of two dynamical systems among which one is slow and one is fast, coupled by diffusive function. By tuning the parameters in concern we report amplitude death as the main result and other emergent dynamics such as frequency synchronization, two frequency state etc. As an important special case, we revisit the well-known model of coupled ocean atmosphere system used in climate studies for the interactive dynamics of a fast oscillating atmosphere and slowly changing ocean that indicates occurrence of multi stable periodic states and steady states of convection coexisting in the system. *

In this context of complex networks, where topology plays an important role on dynamics, we have studied Erdos-Renyi , Scale-free and fully connected regular networks consisting of slow and fast dynamical systems. The study of emergent dynamics on possible motifs present in a network gives the information of the emergent dynamics we see at large. In scale free network , the spread of slowness resulting in desynchronization followed by self organization is studied when one node of the network becomes slow after the whole network was initially synchronized. In scale free network we have also studied the emergence of dynamics with a distribution of time scales where the time scale is inversely proportional to the degree of the node.

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