Sandrine Ngamga (Université de Dschang, Cameroun)

Title: The chimera states in a network of Huygens pendulums examined with Gopal’s indices and recurrence analysis

Abstract: 

Chimera states, defined by the coexistence of coherent and incoherent domains in coupled oscillator networks, arise in a wide variety of systems and play a key role in understanding symmetry breaking, partial synchronisation, and stability in extended dynamical networks. Their emergence has been widely reported in chemical, biological, and electronic systems, but remains far less explored in purely mechanical oscillators, despite their relevance for structural dynamics, robotic assemblies and mechanical metamaterials. In this work, we investigate the collective behaviour of a one-dimensional network of self-sustained Huygens pendulums and demonstrate the emergence of several chimera regimes. Besides classical chimera and multi- chimera patterns, we identify three additional forms : (i) a Quasi-Coherent Chimera, where a weakly perturbed coherent domain coexists with a highly agitated incoherent region; (ii) a Multi-Cluster Chimera, consisting of several coherent clusters separated by incoherent bands ; and (iii) a new EvenOdd Structured Chimera, in which coherent oscillators form two interlaced spatial clusters. This last state cannot be detected by the standard Gopal indicators : the Strength of Incoherence (S) and the Discontinuity Measure (DM) because their nearest-neighbour formulation suppresses the evenodd alternation. To overcome this limitation, we propose a modified version of Gopals indices, which successfully identifies the EvenOdd Structured Chimera. Independent validation using Recurrence Quantification Analysis (RQA) to confirm the coherent and incoherent organisation for all chimera types. These results show that mechanical oscillator networks can host an unexpectedly rich variety of chimera states, and that combining modified local indicators with recurrence-based diagnostics provides a robust framework for detecting both standard and highly structured chimera patterns.

This seminar will take place in Room S08 at the Faculty of Sciences.