https://doi.org/10.1140/epjp/s13360-026-07728-z
Regular Article
Rich nonlinear dynamics of memristively coupled Chialvo maps using a novel second-order discrete memristor
1
Center for Cognitive Science, Trichy SRM Medical College Hospital and Research Center, Trichy, India
2
Center for Research, Easwari Engineering College, Chennai, India
3
Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
4
Center for Research, SRM TRP Engineering College, Trichy, India
5
Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
6
Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
a
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Received:
28
February
2026
Accepted:
20
April
2026
Published online:
10
May
2026
Abstract
This paper introduces a novel voltage-controlled second-order discrete memristor with two internal state variables and a locally active operating region, designed to enrich memory-dependent nonlinear dynamics beyond conventional first-order devices. Power-off plot analysis reveals distinct stability properties for the internal states, where one state exhibits volatile behavior, while the other is non-volatile, resulting in a hybrid short- and long-term memory mechanism. This coexistence of volatile and persistent memory enhances the dynamical flexibility of the device. As an application, the memristor is employed as a synaptic element to couple two Chialvo neuron maps, forming a memristively coupled neural system with increased dimensionality and complexity. The collective dynamics are investigated using bifurcation diagrams, Lyapunov exponents, and time-series analysis, revealing resting, periodic, quasi-periodic, chaotic, and hyperchaotic regimes, as well as pronounced multistability and hysteresis. Parameter mismatch between neurons enlarges chaotic regions and produces diverse firing patterns, while synchronization is mainly observed in simple dynamical states. In addition, intermittent large-amplitude spikes that do not satisfy conventional extreme-event criteria are identified and characterized as quasi-extreme dynamics. The influence of additive noise is also examined, demonstrating noise-induced spiking and transitions from periodic to chaotic behaviors. These results show that second-order memristive coupling provides a flexible framework for generating rich neural dynamics, with potential applications in neuromorphic computing and memory-based nonlinear circuits.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
