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Dynamical behavior of pancreatic β cells with memductance flux coupling: Considering nodal properties and wave propagation in the excitable media

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  • Rajgopal, Karthikeyan
  • Karthikeyan, Anitha
  • V.R., Varun Raj

Abstract

The bursting oscillation modes of the pancreatic β cells releases insulin for regulating the glucose level in blood. We modified the Pernarowski’s pancreatic beta cell model by introducing electromagnetic flux since the electrical coupling between the cells induce and exchange magnetic flux effect while it is in a network. Influence of the magnetic flux in dynamics of the electrical activities particularly bursting behavior is studied. we derived the bifurcation plot and calculated the Lyapunov exponent to identify the parameter range, the system oscillating in chaotic region. The bifurcation plot for magnetic flux coefficient and its corresponding Lyapunov spectrum are presented to describe the transition of the system from chaotic bursting to periodic bursting. Significance of the magnetic flux on the modified system is discussed and revealed the influence on dynamical changes. Lyapunov exponents of the two major parameters is presented for understanding the effect of flux on existing parameters. To reinforce the investigation we adopted Hamiltonian energy method and the level of energy accumulation for different states are plotted. A lattice array of NXN is formulated to study the dynamics of the network. The simulation results of the network for different values of the flux coupling coefficient unrevealing the transition of regular pattern into turbulent waves and reduction in amplitude. The provide a better understanding the mechanism of transformation from chaotic bursting to periodic bursting phenomena, we used sample entropy. The complexity changes in every node is captured and plotted for different values of the magnetic flux coefficient. The obtained results described the dynamical changes of the pancreatic beta cells while it exposed to magnetic flux, the chaotic oscillation of the nodes are suppressed as the flux increased. In a network, regular patterns are broken down and turbulent waves bring down the chaotic bursting into periodic bursting. Finally we provided a potential future direction to proceed the research work further.

Suggested Citation

  • Rajgopal, Karthikeyan & Karthikeyan, Anitha & V.R., Varun Raj, 2022. "Dynamical behavior of pancreatic β cells with memductance flux coupling: Considering nodal properties and wave propagation in the excitable media," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010360
    DOI: 10.1016/j.chaos.2022.112857
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    References listed on IDEAS

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    1. Mostaghimi, Soudeh & Nazarimehr, Fahimeh & Jafari, Sajad & Ma, Jun, 2019. "Chemical and electrical synapse-modulated dynamical properties of coupled neurons under magnetic flow," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 42-56.
    2. Yao, Zhao & Zhou, Ping & Alsaedi, Ahmed & Ma, Jun, 2020. "Energy flow-guided synchronization between chaotic circuits," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Rajagopal, Karthikeyan & Wei, Zhouchao & Moroz, Irene & Karthikeyan, Anitha & Duraisamy, Prakash, 2020. "Elimination of spiral waves in a one-layer and two-layer network of pancreatic beta cells using a periodic stimuli," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Meibo Wang & Shaojuan Ma & Xinzhi Liu, 2021. "Hamilton Energy Control for the Chaotic System with Hidden Attractors," Complexity, Hindawi, vol. 2021, pages 1-10, August.
    5. Guo, Shengli & Xu, Ying & Wang, Chunni & Jin, Wuyin & Hobiny, Aatef & Ma, Jun, 2017. "Collective response, synapse coupling and field coupling in neuronal network," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 120-127.
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