New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds
Since the research of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization helps to explore how complex networks (CNs) work toget...
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2025-02-01
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| author | Anran Zhou Chongming Yang Chengbo Yi Hongguang Fan |
| author_facet | Anran Zhou Chongming Yang Chengbo Yi Hongguang Fan |
| author_sort | Anran Zhou |
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| description | Since the research of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization helps to explore how complex networks (CNs) work together to produce complex behaviors, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization task for uncertain time-delayed CNs is studied in our work. Especially, bounded external perturbations and variable delays of unknown bounds containing coupling delays, internal delays, and pulse delays are all taken into consideration, making the model more general. Through the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-stable theory together with the hybrid impulsive control technique, the problems caused by uncertain inner couplings, time-varying delays, and perturbations can be solved, and novel synchronization criteria are gained for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization of the considered CNs. Different from traditional models, it is not necessary for the coupling matrices to meet the zero-row-sum condition, and the control protocol relaxes the constraint of time delays on impulse intervals. Moreover, numerical experiments and image encryption algorithms are carried out to verify our theoretical results’ effectiveness. |
| format | Article |
| id | doaj-art-c9524341602b4645a146a3e97b2a0082 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-c9524341602b4645a146a3e97b2a00822025-08-20T03:43:30ZengMDPI AGAxioms2075-16802025-02-0114316110.3390/axioms14030161New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown BoundsAnran Zhou0Chongming Yang1Chengbo Yi2Hongguang Fan3College of Computer, Chengdu University, Chengdu 610106, ChinaThe Training Center, Shenzhen Polytechnic University, Shenzhen 518055, ChinaSchool of Undergraduate Education, Shenzhen Polytechnic University, Shenzhen 518055, ChinaCollege of Computer, Chengdu University, Chengdu 610106, ChinaSince the research of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization helps to explore how complex networks (CNs) work together to produce complex behaviors, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization task for uncertain time-delayed CNs is studied in our work. Especially, bounded external perturbations and variable delays of unknown bounds containing coupling delays, internal delays, and pulse delays are all taken into consideration, making the model more general. Through the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-stable theory together with the hybrid impulsive control technique, the problems caused by uncertain inner couplings, time-varying delays, and perturbations can be solved, and novel synchronization criteria are gained for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>-synchronization of the considered CNs. Different from traditional models, it is not necessary for the coupling matrices to meet the zero-row-sum condition, and the control protocol relaxes the constraint of time delays on impulse intervals. Moreover, numerical experiments and image encryption algorithms are carried out to verify our theoretical results’ effectiveness.https://www.mdpi.com/2075-1680/14/3/161complex systems<i>?</i>-synchronizationuncertain inner couplingshybrid impulsive controlexternal perturbations |
| spellingShingle | Anran Zhou Chongming Yang Chengbo Yi Hongguang Fan New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds Axioms complex systems <i>?</i>-synchronization uncertain inner couplings hybrid impulsive control external perturbations |
| title | New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds |
| title_full | New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds |
| title_fullStr | New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds |
| title_full_unstemmed | New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds |
| title_short | New <i>μ</i>-Synchronization Criteria for Nonlinear Drive–Response Complex Networks with Uncertain Inner Couplings and Variable Delays of Unknown Bounds |
| title_sort | new i μ i synchronization criteria for nonlinear drive response complex networks with uncertain inner couplings and variable delays of unknown bounds |
| topic | complex systems <i>?</i>-synchronization uncertain inner couplings hybrid impulsive control external perturbations |
| url | https://www.mdpi.com/2075-1680/14/3/161 |
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