Discrete Dynamics in Nature and Society

Research Article

Lyapunov Stability in the Cournot Duopoly Game

Table 3

Numerical simulation results if (a, b) g UCF.
Track (1)Track (2)Track (3)Track (4)Track (5)
(x0, y0)( + 1,  − 1)( + 0.1,  − 0.1)( + 0.12,  − 0.12)( + 0.13,  − 0.13)( + 0.14,  − 0.14)
(x1, y1)(1.2138, 6.6068)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334,4.8573)
(x2, y2)(0.0299, 5.6538)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x3, y3)(0.4856, 1.0471)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x4, y4)(1.5950, 3.8581)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x5, y5)(1.2135, 6.2775)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x6, y6)(0.1917, 5.6531)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x7, y7)(0.4859, 2.5374)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x8, y8)(1.5755, 3.8592)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x9, y9)(1.2131, 6.2487)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x10, y10)(0.2056, 5.6525)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x11, y11)(0.4862, 1.6208)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x12, y12)(1.5591, 3.8602)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x13, y13)(1.2127, 6.2243)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x14, y14)(0.2174, 5.6518)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x15, y15)(0.4865, 2.6889)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x16, y16)(1.5450, 3.8613)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x17, y17)(1.2124, 6.2031)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x18, y18)(0.2276, 5.6512)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x19, y19)(0.4868, 2.7463)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x20, y20)(1.5362, 3.8623)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x21, y21)(1.2129, 6.1843)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x22, y22)(0.2367, 5.6505)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x23, y23)(0.4871, 2.7958)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x24, y24)(1.5215, 3.8634)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x25, y25)(1.2116, 6.1674)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x26, y26)(0.2448, 5.6498)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x27, y27)(0.4871, 2.8393)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x28, y28)(1.5114, 3.8644)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
(x29, y29)(1.2133, 6.1520)(0.8745, 5.0888)(0.8375, 4.8811)(0.8337, 4.8594)(0.8334, 4.8573)
(x30, y30)(0.2522, 5.6492)(0.7358, 4.9546)(0.8234, 4.8670)(0.8323, 4.8580)(0.8332, 4.8571)
(x31, y31)(0.4877, 2.8781)(0.7926, 4.6111)(0.9292, 4.8328)(0.8329, 4.8546)(0.8333, 4.8568)
(x32, y32)(1.5022, 3.8654)(0.9333, 4.7570)(0.8433, 4.8470)(0.8343, 4.8560)(0.8334, 4.8569)
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StateDisordered4-period4-period4-period4-period