Article
Mathematics, Interdisciplinary Applications
Anitha Karthikeyan, Irene Moroz, Karthikeyan Rajagopal, Prakash Duraisamy
Summary: The study focuses on the dynamical behavior of a temperature affected Morris-Lecar (ML) neuron model. It was found that temperature affected ionic channels lead to various types of oscillations. The bifurcation patterns were well discussed using corresponding Lyapunov exponents.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Electrical & Electronic
Weiwei Fan, Xiongjian Chen, Huagan Wu, Ze Li, Quan Xu
Summary: This paper investigates the dynamics of a 3D Morris-Lecar neuron model with a memristive autapse and finds that the memristive autapse can change the firing period and dynamics of the neuron. It is also discovered that increasing the autapse time delay expands the chaotic regions and leads to the emergence of multistability. Additionally, the study explores the synchronization of coupled memristive autaptic neurons and shows that considering the memristive autapse enhances the synchronization of chaotic neurons, with higher autapse gain reducing the required coupling strength for synchronization.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2023)
Article
Mathematics, Applied
V. V. Klinshov, S. Yu. Kirillov, V. I. Nekorkin, M. Wolfrum
Summary: This study investigates the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. A complex bifurcation scenario with different dynamical regimes is identified through numerical bifurcation analysis, with additional dynamical features such as collective excitability and noise-induced switching and bursting in systems of finite size. The dependence of characteristic quantities on noise level is shown to be non-monotonic.
Article
Physics, Multidisciplinary
Xinying Li, Zongkai Yang, Shaoze Sun, Yufang Gong
Summary: A novel bistable locally active memristor is proposed in this paper, and it is used to simulate the autapse of a neuron. The dynamic analysis methods are used to analyze the equilibrium point, stability, firing mode, and bifurcation characteristics of the system, revealing the coexisting firing patterns in the constructed neuron model.
Article
Mathematics, Interdisciplinary Applications
Guoyuan Qi, Yu Wu, Jianbing Hu
Summary: This paper focuses on proposing a memristive Morris-Lecar neuron model and demonstrates the impact of different intensities of electromagnetic fields on the electrical activity patterns of neurons through numerical simulation. Additionally, the transition trend of neuron firing patterns is investigated using interspike interval analysis and other methods.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Neurosciences
Barna Dudok, Peter M. Klein, Ernie Hwaun, Brian R. Lee, Zizhen Yao, Olivia Fong, John C. Bowler, Satoshi Terada, Fraser T. Sparks, Gergely G. Szabo, Jordan S. Farrell, Jim Berg, Tanya L. Daigle, Bosiljka Tasic, Jordane Dimidschstein, Gord Fishell, Attila Losonczy, Hongkui Zeng, Ivan Soltesz
Summary: Interneurons expressing cholecystokinin (CCK) and parvalbumin (PV) play important roles in regulating hippocampal pyramidal cell output. The activity of CCK BCs in the CA1 of the mouse hippocampus scales inversely with PV and pyramidal cell activity at behaviorally relevant timescales. This inverse coupling is mediated through powerful inhibitory control of CCK BCs by PV cells, demonstrating a novel form of brain-state-specific segregation of inhibition during spontaneous behavior.
Article
Mathematics, Interdisciplinary Applications
Ali Calim, Veli Baysal
Summary: In this study, we investigate the phenomenon of chaotic resonance, in which the response of a neuron to a weak signal is amplified with the assistance of chaotic current generated from background activity in the brain. Our analysis reveals that the quality of signal detection can be greatly improved by considering the contribution of astrocytes, the most abundant types of glial cells, which regulate electrophysiological events in the neuronal medium. We demonstrate that astrocytic glutamate release induced by depolarization can significantly enhance chaotic resonance performance when there is a strong interaction between the astrocyte and the excitable neuron receiving a weak signal with a relatively higher frequency. Additionally, we find that a moderate production rate of gliotransmitters is necessary for the astrocyte to affect the resonance performance of the neuron. Our findings provide new insights into the functioning of astrocyte-neuron circuits, particularly in encoding weak signals through chaotic resonance, and emphasize the key role of astrocytes in regulating and selecting neuronal information processing.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Igor Franovic, Sebastian Eydam
Summary: Patched patterns, a new class of patterns in arrays of non-locally coupled excitable units with attractive and repulsive interactions, involve the formation of majority and minority patches characterized by uniform average spiking frequencies. Chaos typically emerges in patched patterns via torus breakup, with chaotic interfaces developing between units with average frequencies in between those of majority and minority patches. The maximal Lyapunov exponent of chaotic patched patterns converges to a finite value with system size, and patterns with smaller wavenumber may exhibit diffusive motion of chaotic interfaces similar to incoherent chimeras.
Article
Engineering, Mechanical
Chenxi Shang, Kehui Sun, Huihai Wang, Zhao Yao, Shaobo He
Summary: This paper investigates the dynamics of the Rulkov neuron model in a discrete memristor neural network, and analyzes different firing cases through bifurcation diagrams, Lyapunov exponents, and firing modes. The phase synchronization between two neurons coupled by a discrete memristor is analyzed, and chimera states are studied in a discrete memristor ring neural network. Additionally, target waves and spiral waves are generated in a discrete memristor lattice neural network. Simulation results show that the discrete memristor functions well as a synapse, controlling the synchronous behaviors of networks and displaying similar spatial patterns to biological neurons. These findings shed light on the construction of artificial networks and neuromorphic architectures.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Electrical & Electronic
Alexander J. Leigh, Moslem Heidarpur, Mitra Mirhassani
Summary: A highly accurate digital implementation of the Morris-Lecar neuron model is proposed for hardware acceleration in neuroscience simulation. The implementation utilizes the COordinate Rotation DIgital Computer (CORDIC) algorithm to create a fixed-point implementation that is both highly accurate and requires low digital hardware resources. Compared to the current state-of-the-art, this design achieves higher accuracy, requires fewer hardware resources, and operates at a higher maximum clock frequency. The design is validated on FPGA with a normalized RMSE of 0.2039 at a maximum clock frequency of 378.07MHz.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2022)
Article
Physics, Multidisciplinary
Tao Li, Lin Yan, Zhigang Zheng
Summary: Studies of sustained oscillations on complex networks with excitable node dynamics have attracted much attention in recent years. This paper proposes a functional-weight approach that extends the study of sustained oscillations in gene-regulated networks to high-dimensional node dynamics. By testing different types of networks, it is found that this approach accurately identifies the oscillation source and propagation path.
Article
Engineering, Mechanical
Subhashis Das, Madhurima Mukherjee, Argha Mondal, Kshitish Ch. Mistri, Sanat Kumar Mahato, M. A. Aziz-Alaoui
Summary: This article demonstrates an analytical approach to show the emerging traveling pulses for the local evolution of a set of diffusively coupled dynamical equations representing neuronal impulses. The derived dynamics governing the traveling pulses solution is described in a space-time reference frame with a two-dimensional excitable Hindmarsh-Rose (H-R) type oscillator. The conditions that allow us to describe explicitly the nature of propagating traveling pulses are deduced. The obtained results reveal the possibility of collective behavior for information processing in excitable systems.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Justus A. Kromer
Summary: In excitable systems, the interplay of noise, feedback, and input from other elements can lead to asynchronous bursting of individual elements and collective bursting of the entire network. For a fixed noise intensity, sparse collective event generation is observed in large networks, while small networks exhibit rapid collective event generation. Collective bursting occurs for intermediate network sizes.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2021)
Article
Multidisciplinary Sciences
Guy Blondeau Soh, Robert Tchitnga, Paul Woafo
Summary: This study investigated the influence of long-range interaction parameter on the excitability threshold in a ring of FHN system through analytical and numerical studies. The results showed that long-range coupling enhanced the threshold parameter range and affected the network dynamics. Additionally, different effects were observed when considering bidirectional and unidirectional coupling, leading to traveling patterns and multi-chimera states, respectively. The study also compared the dynamics of coupled oscillators and excitable neurons, revealing differences in oscillation period based on the coupling parameter values.
Article
Mathematics, Interdisciplinary Applications
Lixing Lei, Junzhong Yang
Summary: The study investigates emergent patterns on duplex networks by studying the coupled FitzHugh-Nagumo model, finding that dominant network modes on duplex networks are related to the most unstable network modes in monolayer networks, and developing approximation methods to address the instability of homogeneous equilibrium on duplex networks, which could serve as a tool for analyzing patterns on duplex networks.
CHAOS SOLITONS & FRACTALS
(2021)
