@@ -1201,17 +1201,22 @@ k1 = -0.17, k2 = -0.17, k_el = 0.0, xv = 2.0)
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```
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```math
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\\ begin{aligned}
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- \\ dot x_{i} = y_{i} + bx^{2}_{i} - ax^{3}_{i} - z_{i} + I - k_{i}(x_{i} - v_{s})\\ Gamma(x_{j}) + k(x_{j} - x_{i})\\\\
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- \\ dot y_{i} = c - d x^{2}_{i} - y_{i}\\\\
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- \\ dot z_{i} = r[s(x_{i} - x_{R}) - z_{i}]\\\\
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- \\ i,j=1,2 (i\\ neq j).\\\\
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+ \\ dot x_{i} &= y_{i} + bx^{2}_{i} - ax^{3}_{i} - z_{i} + I - k_{i}(x_{i} - v_{s})\\ Gamma(x_{j}) + k(x_{j} - x_{i})\\\\
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+ \\ dot y_{i} &= c - d x^{2}_{i} - y_{i}\\\\
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+ \\ dot z_{i} &= r[s(x_{i} - x_{R}) - z_{i}]\\\\
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\\ end{aligned}
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```
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+ where ``i,j=1,2 (i\\ neq j)`` denote two oscillators.
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The two coupled Hindmarsh Rose element by chemical and electrical synapse.
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- it is modelling the dynamics of a neuron's membrane potential.
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+ It is modelling the dynamics of a neuron's membrane potential.
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The default parameter values are taken from article "Dragon-king-like extreme events in
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- coupled bursting neurons", DOI:https://doi.org/10.1103/PhysRevE.97.062311.
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+ coupled bursting neurons", from [^Mishra2018].
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+
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+ [^Mirshra2018]:
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+ A. Mishra, S. Saha, M. Vigneshwaran, P. Pal, T. Kapitaniak, and S. K. Dana,
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+ "Dragon-king-like extreme events in coupled bursting neurons",
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+ Phys. Rev. E, vol. 97, no. 6, p. 062311, Jun. 2018, doi: 10.1103/PhysRevE.97.062311.
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"""
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function hindmarshrose_two_coupled (u0= [0.1 , 0.2 , 0.3 , 0.4 , 0.5 , 0.6 ];
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a = 1.0 , b = 3.0 , c= 1.0 , d = 5.0 , r = 0.001 , s = 4.0 , xr = - 1.6 , I = 4.0 ,
@@ -1366,14 +1371,15 @@ Pacific barnacle [^MorrisLecar1981]. Its evolution is given by:
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```math
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\\ begin{aligned}
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\\ dot{V} &= -g_{Ca} M(V) (V - V_{Ca}) - g_K N (V - V_K) - g_L (V - V_L) + I \\\\
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- \\ dot{N} &= (-N + G(V)) / \t au \\\\
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+ \\ dot{N} &= (-N + G(V)) / \\ tau \\\\
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\\ end{aligned}
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```
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with
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```math
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\\ begin{aligned}
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- M(V) = 0.5 (1 + \\ tanh((x-V1)/V2)) \\\\
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- G(V) = 0.5 (1 + \\ tanh((x-V3)/V4)) \\\\
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+ M(V) &= 0.5 (1 + \\ tanh((x-V1)/V2)) \\\\
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+ G(V) &= 0.5 (1 + \\ tanh((x-V3)/V4)) \\\\
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+ \\ end{aligned}
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```
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[^IzhikevichBook]:
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