{"id":{"repo_id":"cambridge","oai_identifier":"oai:www.repository.cam.ac.uk:1810/306692"},"canonical_url":"https://search.dev.ndltd.org/etd/cambridge/oai:www.repository.cam.ac.uk:1810/306692","repository":{"repo_id":"cambridge","name":"Cambridge University","base_url":"https://api.repository.cam.ac.uk/server/oai/request"},"display":{"title":"Nonlinear resonance and excitability in interconnected systems","abstract":"Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. While in the context of equilibrium dynamics there is a well-developed theory that can account for robustness and optimality in this process, we still lack a corresponding methodology for nonequilibrium dynamics and in particular oscillatory behaviours. With the aim of fostering such a theory, this thesis studies two basic interconnections in the contexts of nonlinear resonance and excitability, two phenomena with the potential of encompassing a large number of applications. The first interconnection is considered in the context of vibration absorption. It corresponds to coupling two Duffing oscillators, the prototypical example of nonlinear resonator. Of primary interest is the frequency response of the system, which quantifies the behaviour in presence of harmonic forces. The analysis focuses on how isolated families of solutions appear and merge with a main one. Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods. The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. Following this, the analysis moves to the complete interconnection, and in particular on how it can generate different patterns of bursting activity.","abstract_html":"Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. While in the context of equilibrium dynamics there is a well-developed theory that can account for robustness and optimality in this process, we still lack a corresponding methodology for nonequilibrium dynamics and in particular oscillatory behaviours. With the aim of fostering such a theory, this thesis studies two basic interconnections in the contexts of nonlinear resonance and excitability, two phenomena with the potential of encompassing a large number of applications. The first interconnection is considered in the context of vibration absorption. It corresponds to coupling two Duffing oscillators, the prototypical example of nonlinear resonator. Of primary interest is the frequency response of the system, which quantifies the behaviour in presence of harmonic forces. The analysis focuses on how isolated families of solutions appear and merge with a main one. Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods. The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. Following this, the analysis moves to the complete interconnection, and in particular on how it can generate different patterns of bursting activity.","abstract_has_math":false,"creators":["Cirillo, Giuseppe Ilario"],"institution":"University of Cambridge","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Sepulchre, Rodolphe"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-10-01","date_published":"2019-10-01","updated_at":"2026-07-22T22:24:17Z","subjects":["Nonliear resonance","Excitability","Interconnection"],"languages":["eng"],"rights":[],"rights_urls":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/c7dbd85c-a1fd-42f6-a15f-fc7138fd09c5/download","https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.17863/CAM.53779","outbound_label":"DOI","outbound_source":"dc:identifier.doi"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sepulchre, Rodolphe"]},{"key":"dc:creator","label":"Author","values":["Cirillo, Giuseppe Ilario"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2019-10-01"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cambridge"]},{"key":"dc:relation.isreferencedby.uri","label":"Dc Relation Isreferencedby URI","values":["https://www.repository.cam.ac.uk/handle/1810/306692"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Nonliear resonance","Excitability","Interconnection"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/c7dbd85c-a1fd-42f6-a15f-fc7138fd09c5/download","https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.17863/CAM.53779"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/a4489d3f-5073-4d35-b176-13db91057063/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Engineering design amounts to develop components and interconnect them to obtain a desired behaviour. 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Using singularity theory it is possible to organise these solutions in the space of parameters and delimit their presence through numerical methods. The second interconnection studied in this dissertation appears in the context of excitable circuits. Combining a fast excitable system and a slower oscillatory system that share a similar structure naturally leads to bursting. The resulting system has a slow-fast structure that can be leveraged in the analysis. The first step of this analysis is a novel slow-fast model of bistability between a rest state and a spiking attractor. 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