The formed patterns due to blocking in ion channels in calcium.

<p>The developed state (<i>t</i> = 800 time units) when some channels of calcium in neurons in a square array (95≤<i>i</i> ≤100, 95≤<i>j</i> ≤100) is blocked at <i>x</i>_k = 1, coupling intensity <i>D</i> = 4, for <i>x</i>_Ca = 0.1 (panel a), <i>x</i>_Ca = 0.2 (panel b).</p

The development of spiral wave under different channel noise when the target wave is broken by artificial defects.

<p>Artificial defects area is within 90≤<i>i</i> ≤95, 1≤<i>j</i> ≤100 (<i>V_ij</i> = 0). The area forced by external currents with diversity is close to the center of the network (90≤<i>i</i> ≤100, 90≤<i>j</i> ≤100). For <i>I</i>₀ = 90,<i>N</i>₀ = 200 (panel a) ; <i>I</i>₀ = 90,<i>N</i>₀ = 250 (panel b) ; <i>I</i>₀ = 110,<i>N</i>₀ = 200 (panel c) ; <i>I</i>₀ = 110,<i>N</i>₀ = 250 (panel d) ; at <i>I</i>₂ = 40, coupling intensity <i>D</i> = 2, transient period <i>t</i> = 800 and no-flux boundary condition is used.</p

The distribution of forcing currents with diversity vs. forcing area for generating a target wave.

<p>The threshold for initiating a target wave in the network in the two-parameter space for square size forced by current <i>I</i>₀ and gradient current Δ<i>I</i> = <i>I</i>₀−<i>I</i>₁.</p

The development of spiral wave under certain channel noise (channel number <i>N₀</i> = 1000) when the target wave is broken by local poisoned area.

<p>Blocked area is within 90≤<i>i</i> ≤95, 1≤<i>j</i> ≤100. The area forced by external currents with diversity is close to the center of the network (90≤<i>i</i> ≤95, 90≤<i>j</i> ≤95), <i>I</i>₀ = 60,<i>I</i>₂ = 40, for <i>x</i>_k = 0.1 (panel a) ; <i>x</i>_k = 0.2 (panel b), <i>x</i>_k = 0.3 (panel c), <i>x</i>_k = 0.4 (panel d), <i>x</i>_k = 0.5 (panel e), <i>x</i>_k = 0.6 (panel <i>f</i>), coupling intensity <i>D</i> = 2, transient period <i>t</i> = 800 and no-flux boundary condition is used.</p

The formed target wave induced by forcing currents with diversity.

<p>The forcing current <i>I</i>₀ = 41, coupling intensity <i>D</i> = 4, S = 3×3 (90≤<i>i</i> ≤92, 90≤<i>j</i>≤92), <i>I</i>₁ = 40, transient period <i>t</i> = 800 time units and no-flux boundary condition is used.</p

The formed patterns under forcing currents with diversity and blocking in ion channels in calcium.

<p>The developed state (<i>t</i> = 800 time units) when some channels of calcium in neurons in a square array (90≤<i>i</i> ≤95, 1≤<i>j</i> ≤100) is blocked at <i>x</i>_k = 1, for <i>x</i>_Ca = 0.1 (panel a), <i>x</i>_Ca = 0.2 (panel b), <i>x</i>_Ca = 0.3 (panel c) ,<i>x</i>_Ca = 0.4 (panel d) ; the forcing currents with diversity are imposed on the local area 95≤<i>i</i> ≤100, 100≤<i>j</i> ≤105 with <i>I</i>₀ = 60, <i>I</i>₁ = 40 for other nodes, coupling intensity <i>D</i> = 4.</p

The formed target wave induced by forcing currents with diversity.

<p>The coupling intensity <i>D</i> = 4, S = 7×7 (90≤<i>i</i> ≤96, 90≤<i>j</i>≤96), <i>I</i>₁ = 40, for <i>I</i>₀ = 49 (panel a), <i>I</i>₀ = 51 (panel b), <i>I</i>₀ = 53 (panel c), <i>I</i>₀ = 55 (panel d), transient period <i>t</i> = 800 time units and no-flux boundary condition is used.</p

Formation of target wave induced by ion channels blocking in potassium.

<p>The developed state (<i>t</i> = 800 time units) when some potassium ion channels in a square array (90≤<i>i</i> ≤100, 90≤<i>j</i> ≤100) are blocked at <i>x</i>_Ca = 1, coupling intensity <i>D</i> = 4, for <i>x</i>_k = 0.1 (panel a), <i>x</i>_k = 0.2 (panel b),<i>x</i>_k = 0.3 (panel c), <i>x</i>_k = 0.4 (panel d).</p

The distribution of factor of synchronization vs. forcing currents with diversity.

<p>The size of local area forced with current <i>I</i>₀ is marked as <i>S</i> = 9 (90≤<i>i</i> ≤92, 90≤<i>j</i> ≤92), <i>S</i> = 16 (90≤<i>i</i> ≤93, 90≤<i>j</i> ≤93), <i>S</i> = 25 (90≤<i>i</i> ≤94, 90≤<i>j</i> ≤94), <i>S</i> = 36 (90≤<i>i</i> ≤95, 90≤<i>j</i> ≤95), <i>S</i> = 49 (90≤<i>i</i> ≤96, 90≤<i>j</i> ≤96), coupling intensity <i>D</i> = 4 and transient period is about 800 time units.</p

The evolution of spiral wave under different additive Gaussian white noise.

<p>Blocked area is within 90≤<i>i</i> ≤95, 1≤<i>j</i> ≤100, <i>x</i>_k = 0.3. The area forced by external currents with diversity is within the area 90≤<i>i</i>≤95, 90≤<i>j</i> ≤95, <i>I</i>₀ = 60, <i>I</i>₁ = 40, for noise intensity <i>D_noise = </i>100 (panel a) ; <i>D_noise = </i>200 (panel b) ; <i>D_noise = </i>300 (panel c) ; <i>D_noise = </i>500 (panel d), coupling intensity <i>D</i> = 2, transient period <i>t</i> = 800 and no-flux boundary condition is used.</p