1. Discrete memristive Hindmarsh-Rose neural model with fractional-order differencesFatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2025, original scientific article Abstract: Discrete systems can offer advantages over continuous ones in certain contexts, particularly in terms of simplicity and reduced computational costs, though this may vary depending on the specific application and requirements. Recently, there has been growing interest in using fractional differences to enhance discrete models' flexibility and incorporate memory effects. This paper examines the dynamics of the discrete memristive Hindmarsh-Rose model by integrating fractional-order differences. Our results highlight the complex dynamics of the fractional-order model, revealing that chaotic firing depends on both the fractional-order and magnetic strength. Notably, certain magnetic strengths induce a transition from periodic firing in the integer-order model to chaotic behavior in the fractional-order model. Additionally, we explore the dynamics of two coupled discrete systems, finding that electrical coupling leads to the synchronization of chaotic dynamics, while chemical coupling ultimately results in a quiescent state.
Keywords: memristive Hindmarsh-Rose model, discrete systems, fractional-order differences
Published in DKUM: 06.05.2025; Views: 0; Downloads: 0
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2. Minimal universal laser network model : synchronization, extreme events, and multistabilityMahtab Mehrabbeik, Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, Riccardo Meucci, 2024, original scientific article Abstract: The synchronization of chaotic systems has garnered considerable attention across various fields, including neuroscience and physics. Particularly in these domains, synchronizing physical systems such as laser models is crucial for secure and rapid information transmission. Consequently, numerous studies investigate the synchronizability of different laser networks by establishing logical network frameworks. In this study, we employed a minimal universal laser (MUL) model designed to capture the essential dynamics of an actual laser model within just three dimensions. Within the network model of MUL systems, we introduced the linear diffusive function of neighboring nodes' fast variables into the feedback term of the lasers, with models arranged in a global network structure. Our examination of synchronization within the constructed MUL network utilized master stability functions and the time-averaged synchronization error index. The findings suggest that while the network fails to achieve complete synchrony, it exhibits various synchronization phenomena, including cluster synchronization, chimera states, extreme events, and multistability. These results shed light on the complex dynamics underlying the synchronization of chaotic systems in networked environments, offering insights relevant to numerous applications across diverse fields.
Keywords: minimal universal laser model, synchronization, extreme events
Published in DKUM: 16.12.2024; Views: 0; Downloads: 4
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3. Interlayer and intralayer synchronization in multiplex fractional-order neuronal networksBo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2022, original scientific article Abstract: Fractional-order models describing neuronal dynamics often exhibit better compatibility with diverse neuronal firing patterns that can be observed experimentally. Due to the overarching significance of synchronization in neuronal dynamics, we here study synchronization in multiplex neuronal networks that are composed of fractional-order Hindmarsh-Rose neurons. We compute the average synchronization error numerically for different derivative orders in dependence on the strength of the links within and between network layers. We find that, in general, fractional-order models synchronize better than integer-order models. In particular, we show that the required interlayer and intralayer coupling strengths for interlayer or intralayer synchronization can be weaker if we reduce the derivative order of the model describing the neuronal dynamics. Furthermore, the dependence of the interlayer or intralayer synchronization on the intralayer or interlayer coupling strength vanishes with decreasing derivative order. To support these results analytically, we use the master stability function approach for the considered multiplex fractional-order neuronal networks, by means of which we obtain sufficient conditions for the interlayer and intralayer synchronizations that are in agreement with numerical results.
Keywords: synchronization, neuronal network, multilayer network, neuronal dynamics
Published in DKUM: 28.05.2024; Views: 230; Downloads: 8
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