Analysis of spatially extended excitable Izhikevich neuron model near instability |
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Authors: | Mondal Arnab Mondal Argha Sharma Sanjeev Kumar Upadhyay Ranjit Kumar |
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Institution: | 1.Dipartimento di Architettura, Roma Tre University, Via Madonna dei Monti 40, Roma, Italy ;2.Department of Structures for Engineering and Architecture, University of Naples Federico II, Via Claudio, 21, 80124, Naples, Italy ;3.Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via Eudossiana 18, Roma, Italy ; |
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Abstract: | The dynamic response and bifurcations of high-dimensional systems endowed with hysteretic restoring forces in all degrees of freedom are investigated. Two types of hysteresis models are considered, namely the Bouc–Wen model and a differential version of the so-called exponential model of hysteresis. The numerical technique tailored for tackling high-dimensional hysteretic systems is based on an enhanced pathfollowing approach based on the Poincaré map. In particular, a five-dof mass-spring-damper-like system, with each rheological element described by the Bouc–Wen or the exponential model of hysteresis enriched by cubic and quintic nonlinear elastic terms, is investigated and a rich variety of nonlinear responses and bifurcations is found and discussed. |
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