1. Discrete memristive Hindmarsh-Rose neural model with fractional-order differencesFatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2025, izvirni znanstveni članek Opis: 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.
Ključne besede: memristive Hindmarsh-Rose model, discrete systems, fractional-order differences
Objavljeno v DKUM: 06.05.2025; Ogledov: 0; Prenosov: 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, izvirni znanstveni članek Opis: 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.
Ključne besede: minimal universal laser model, synchronization, extreme events
Objavljeno v DKUM: 16.12.2024; Ogledov: 0; Prenosov: 4
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3. Synchronization in simplicial complexes of memristive Rulkov neuronsMahtab Mehrabbeik, Sajad Jafari, Matjaž Perc, 2023, izvirni znanstveni članek Opis: Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.
Ključne besede: simplicial complex, higher-order network, memristive Rulkov, synchronization, cluster synchronization
Objavljeno v DKUM: 11.09.2024; Ogledov: 37; Prenosov: 9
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4. Interlayer and intralayer synchronization in multiplex fractional-order neuronal networksBo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, 2022, izvirni znanstveni članek Opis: 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.
Ključne besede: synchronization, neuronal network, multilayer network, neuronal dynamics
Objavljeno v DKUM: 28.05.2024; Ogledov: 230; Prenosov: 8
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5. The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous playersAtefeh Ahmadi, Sourav Roy, Mahtab Mehrabbeik, Dibakar Ghosh, Sajad Jafari, Matjaž Perc, 2023, izvirni znanstveni članek Opis: One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.
Ključne besede: nonlinear dynamics, game theory, stability analysis, public goods
Objavljeno v DKUM: 02.08.2023; Ogledov: 459; Prenosov: 47
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