This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the Gram-Schmidt orthonormalization procedure. We expect two positive LCEs for the Chen System. The program is adaptive to any n-th order chaotic and hyperchaotic systems. Controllers are then developed in order to stablize the hyperchaotic Chen system via linear feedback, speed feedback and nonlinear feedback control and a stability analysis is presented.
","abstract_html":"<p>This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the Gram-Schmidt orthonormalization procedure. We expect two positive LCEs for the Chen System. The program is adaptive to any n-th order chaotic and hyperchaotic systems. Controllers are then developed in order to stablize the hyperchaotic Chen system via linear feedback, speed feedback and nonlinear feedback control and a stability analysis is presented.</p>","abstract_has_math":false,"creators":["Joseph, Adrian G."],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (restricted to Georgia Southern)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Jiehua Zhu","Alex Stokolos"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:27:52Z","subjects":["ETD","Lyapunov exponents","adaptive control","Hyperchaotic","Chen System","Gram-Schmidt","Control Theory","Dynamic Systems","Non-linear Dynamics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1094","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jiehua Zhu","Alex Stokolos"]},{"key":"dc:creator","label":"Author","values":["Joseph, Adrian G."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-04-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (restricted to Georgia Southern)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Lyapunov exponents","adaptive control","Hyperchaotic","Chen System","Gram-Schmidt","Control Theory","Dynamic Systems","Non-linear Dynamics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1094"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the Gram-Schmidt orthonormalization procedure. We expect two positive LCEs for the Chen System. The program is adaptive to any n-th order chaotic and hyperchaotic systems. Controllers are then developed in order to stablize the hyperchaotic Chen system via linear feedback, speed feedback and nonlinear feedback control and a stability analysis is presented.
"]},{"key":"dc:title","label":"Title","values":["Computation of Lyapunov Exponents and Control of a Hyperchaotic System"]}]}],"canonical_facts":{"dc:contributor":["Jiehua Zhu","Alex Stokolos"],"dc:creator":["Joseph, Adrian G."],"dc:date.available":["2014-04-16T07:00:00Z"],"dc:description.abstract":["This paper presents algorithms developed in MATLAB to simulate the hyperchaotic Chen system and also estimates the largest Lyapunov characteristic exponent (LCE) and provides a method to compute the entire Lyapunov spectrum of the dynamical system. The computation of the Lyapunov spectrum relies on calculating the order-p LCEs and repeated application of the Gram-Schmidt orthonormalization procedure. We expect two positive LCEs for the Chen System. The program is adaptive to any n-th order chaotic and hyperchaotic systems. Controllers are then developed in order to stablize the hyperchaotic Chen system via linear feedback, speed feedback and nonlinear feedback control and a stability analysis is presented.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1094"],"dc:subject":["ETD","Lyapunov exponents","adaptive control","Hyperchaotic","Chen System","Gram-Schmidt","Control Theory","Dynamic Systems","Non-linear Dynamics"],"dc:title":["Computation of Lyapunov Exponents and Control of a Hyperchaotic System"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (restricted to Georgia Southern)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:27:52Z"}