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We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf bifurcation point and observe the impact of Gaussian white noise to study its effects on pattern formation. These types of patterns are robust in the excitable model. Our results might contribute significantly to the dynamical studies of irregular neural computation. <\/jats:p>","DOI":"10.1142\/s0218127421300305","type":"journal-article","created":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T06:11:56Z","timestamp":1630563116000},"page":"2130030","source":"Crossref","is-referenced-by-count":14,"title":["Synchronization and Pattern Formation in a Memristive Diffusive Neuron Model"],"prefix":"10.1142","volume":"31","author":[{"given":"Sanjeev Kumar","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India"}]},{"given":"Arnab","family":"Mondal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India"}]},{"given":"Argha","family":"Mondal","sequence":"additional","affiliation":[{"name":"School of Engineering, Amrita Vishwa Vidyapeetham, Amritapuri, Kollam 690525, India"},{"name":"Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1210-7804","authenticated-orcid":false,"given":"Ranjit Kumar","family":"Upadhyay","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India"}]},{"given":"Jun","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Physics, Lanzhou University of Technology, Lanzhou 730050, P. 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