Определение. Замкнутая траектория
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
автономного уравнения (5) называется неустойчивым предельным циклом, если существует такое
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAATCAMAAAAkluS8AAAAAXNSR0ICQMB9xQAAAJ9QTFRFAgICAQEBExMuLhMTMBUVPyY/IyNPIiJOKEFBTyMjTiIiQld3Q1h4RFl5XX2WX3+YeVlEeFhDmH9fkHeEmJismKu8rZmZpI6CvKuYvq2asLjHr7fGucbNwMDNwc3Y2M3Bws7Z2c7C2s/Dw8/a09fg3OPm2+Ll5uPc5eLb/v7+/f398fHu9/j47/Ly8vLv+Pj3+fn4+Pn59vf38PDt////zp4NggAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADPSURBVCjPtdJZD4IwDADgKXigIniDB6fINgQB9/9/m4wdYAKJD9IHktKPrW0A5LcAAznUU0cYo5ZLbj3MAsBBjbOWz07nTtNMc6R7mSNHnNDuIN94hPirQjj3aq55KTBwI+NJxB+1y3epPX4ICBrpz1JCsoXHHTxXyUGeEgC9xF3uWGVb+krep7CsdrHCHbzUJUcyDNX5XfYHRX+niPZo0rHqzUJVL/i8ZvWxpbN5kz2m4bJJkAuEoq3q5VsL2f5swMNge/ladFUMh/xf/uU+itOGWC5vSCUAAAAASUVORK5CYII=)
, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
является -предельным множеством для любой траектории, проходящей через точку из -окрестности кривой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
.
Так как в реальной действительности время течет в положительном направлении, то на практике реализуются те периодические движения, которым соответствуют устойчивые предельные циклы. Такие движения называются автоколебаниями.
Теорема 4. Пусть
![](data:image/png;base64,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)
. (7)
Если
![](data:image/png;base64,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)
, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
является устойчивым предельным циклом; если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACUAAAATCAMAAAAgYzSBAAAAAXNSR0ICQMB9xQAAAKVQTFRFAQEBAgICLhMTMBUVPyY/IyNPIiJOJCRQKEFBUCQkTyMjTiIiXTVMQ1h4RFl5X3+YXn6XeFhDeVlEaURpaWmGl35ehmlph2pqhYWFmq2+may9j6WupY+DvKuYvayZvq2awc3Y2M3Bws7Z2c7C2s/Dw8/aydTOwcHO09fg3OPm5eLb5uPc/f39/v7+8vLv+fn47/Ly+Pn5+Pj35uvp9vf38PDt////1FZ66gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADSSURBVCjPtZLJGoIgFIVBG82oLBssZ6xERC3j/R8tJ4yFixbFgs357+Wc8wH4Nwf8mqI0HRRTIdQUm4PTIGRD6KX9rmwfD1H+OGea11NkV4hx6elsE3AeLgtBOVZlodHx6mMxGcXd1VJm8DBA0EgY9lw4ySvPi0C43z4PsSMCYIhKOkD560ssB0iUWm+pRBGUeYykAJwSdXYXvojwxfQz57aVdkUSFbUDmVG1YKMuY72G6ddbA/kQ9UsxKl9a1PXlVr4TdZq3Tci1uhBG//kTP6LectGE/rt5F1oAAAAASUVORK5CYII=)
, то
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
— неустойчивый предельный цикл.
Характер приближения соседних траекторий к
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAF1QTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CpZulvKuYvayZvq2arq6uv7i4ws7Z2M3B2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////bwK8pAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7JDoAgDARQ3PcNFcWW+f/PFGOEHm0yk7zMpQrilI+9rC/7olQaGFJ6wI3riRPzLsBh1gwfzr0zATxXFOAKjQAsFMG1wJYjYpSYWgHx6A/cID8VwDaRv/0AAAAASUVORK5CYII=)
при
![](data:image/png;base64,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)
следующий: они приближаются к
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAARCAMAAADe472QAAAAAXNSR0ICQMB9xQAAAGBQTFRFAgICXTVMRFl5X3+YXn6XeVlEl35ehXiRhHeQmpqumq2+pI6CppymvKuYvayZvq2arq6uv7i4ws7Z2M3Bw8/a2c7C09fg3OPm4NfT5uPc/v7+/f39+Pn58vLv+fn4////Kp5FrwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABXSURBVBjTjc7HDoAwDAPQsvcehZLU//+XFCHaHIlkS0++REGccjGXcWVe5GoGupgecGVb4ki/C3DoJcGHc2+0B48FedhshQcmCuBSYEsR0EsMtYB49AdubYUWeJ1WFpsAAAAASUVORK5CYII=)
, образуя бесконечное число витков спирали, как изнутри, так и снаружи.
![](data:image/jpeg;base64,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)
2.6. Устойчивость по первому приближению.
Вернемся к рассмотрению уравнения (1), где
![](data:image/png;base64,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)
. После замены
![](data:image/png;base64,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)
получим уравнение (2), которое, используя разложение в ряд Тейлора, запишем в виде
![](data:image/png;base64,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)
, (8)
где
![](data:image/png;base64,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)
при
![](data:image/png;base64,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)
. (9)
Теорема 5. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAMAAADjcdz2AAAAAXNSR0ICQMB9xQAAAHJQTFRFAAAAAgICAgEBPyY/IiJOUCQkQ1h4Qld2RVp5Xn6XdldCl35emH9fg4+lm6WlmKu8mq2+pJqkr7fGws7Z2M3B2c7C18zAw8/a2s/D3OPm5eLb/v7++Pj37/Ly9vf3+Pn5/f399/j49/f2/f3+8vLv////8hZy7gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPhc/JDkBAEATQaTtj301jbP3/v0giYkaEOtThnaoYPcI+AR8gch36oNAAOdOhjM1OBRFV1qBAn421ChgCGI68oWyI+A0ooqO5fy2dancmXIJkPWGzAVJqAcCTf+deYQfu3SKG55MIRQAAAABJRU5ErkJggg==)
— постоянная матрица, предельный переход в (9) выполняется равномерно по
![](data:image/png;base64,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)
и вещественные части собственных чисел матрицы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAMAAADjcdz2AAAAAXNSR0ICQMB9xQAAAHJQTFRFAAAAAgICAgEBPyY/IiJOUCQkQ1h4Qld2RVp5Xn6XdldCl35emH9fg4+lm6WlmKu8mq2+pJqkr7fGws7Z2M3B2c7C18zAw8/a2s/D3OPm5eLb/v7++Pj37/Ly9vf3+Pn5/f399/j49/f2/f3+8vLv////8hZy7gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPhc/JDkBAEATQaTtj301jbP3/v0giYkaEOtThnaoYPcI+AR8gch36oNAAOdOhjM1OBRFV1qBAn421ChgCGI68oWyI+A0ooqO5fy2dancmXIJkPWGzAVJqAcCTf+deYQfu3SKG55MIRQAAAABJRU5ErkJggg==)
отрицательны. Тогда решение
![](data:image/png;base64,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)
уравнения (8) асимптотически устойчиво.
Теорема 6. Пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAMAAADjcdz2AAAAAXNSR0ICQMB9xQAAAHJQTFRFAAAAAgICAgEBPyY/IiJOUCQkQ1h4Qld2RVp5Xn6XdldCl35emH9fg4+lm6WlmKu8mq2+pJqkr7fGws7Z2M3B2c7C18zAw8/a2s/D3OPm5eLb/v7++Pj37/Ly9vf3+Pn5/f399/j49/f2/f3+8vLv////8hZy7gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPhc/JDkBAEATQaTtj301jbP3/v0giYkaEOtThnaoYPcI+AR8gch36oNAAOdOhjM1OBRFV1qBAn421ChgCGI68oWyI+A0ooqO5fy2dancmXIJkPWGzAVJqAcCTf+deYQfu3SKG55MIRQAAAABJRU5ErkJggg==)
— постоянная матрица, предельный переход в (9) выполняется равномерно по
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAD8AAAAYCAMAAAB6KNVjAAAAAXNSR0ICQMB9xQAAANhQTFRFAQEBAgICFRUwMBUVLhMTPyY/JCRQIyNPTiIiTyMjUCQkTDVdXTVMXUw1RFl5Q1h4X3+YXn6XeFhDakVqemt6l35emH9fln1dh2pqhHeQkXiFhoaGmZmtg4+lmpqugo6kmay9mq2+mKu8rpqapY+DpI6CrZmZpJqkvayZvKuYvq2ar7fGxrev2c7Cwc3Yw8/aws7ZzsHB2M3BwcHO2s/D39bS2+Ll2uHk3OPm5eLb5uPc5OHa/v7+/f397vHx8vLv7/Ly+Pn5+fn49vf38fHu5ero7fDw////RWi2KwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFkSURBVDjL1ZRtV4IwGIb3aGWlmVaavZhSWpaiRESDNnnJ2v//R40BOpIXz+FT9wcO596uce/ZwxBLF6GUsB2EMvwOglY+SfL5YdGXH5bleOd8WYpnzm05no3MNU8y+NwzUNsxb01DhwaS+NiXj1XMEuvadVfw5HP/IzCIVQWAAzfmY1/SBCqmtQcwFwVoYMF3EYJFkKfpJfLH/kZ2nzkXJ03P7+GAP9TC/B0lePpPX3/yh76kGcdUpPGFphK/amAR5wggkT/yJb3yMf2Up3TeJP45zO1cecn6C5/I/8HMZOSyxvtmJfH+mSKm+D0zwYf+BIby/qmObtqUjvCmfnb9+1pkNmo/8v6Fb/VFm0QuMwAU1oWwrNH5GVDB61Fp/8KfaEzlS1Vr7nb/6K3i/uUVD2pN3/H2nDEu5l/mTFeYc5xyGazu8v6f+6hHB3SM0++PRzeH5zVqRS9KxoxF3v2xq/47/wv/mXn1pQF+ogAAAABJRU5ErkJggg==)
. Для устойчивости по Ляпунову нулевого решения уравнения (8) необходимо, чтобы вещественные части собственных чисел матрицы
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAMAAADjcdz2AAAAAXNSR0ICQMB9xQAAAHJQTFRFAAAAAgICAgEBPyY/IiJOUCQkQ1h4Qld2RVp5Xn6XdldCl35emH9fg4+lm6WlmKu8mq2+pJqkr7fGws7Z2M3B2c7C18zAw8/a2s/D3OPm5eLb/v7++Pj37/Ly9vf3+Pn5/f399/j49/f2/f3+8vLv////8hZy7gAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABlSURBVCjPhc/JDkBAEATQaTtj301jbP3/v0giYkaEOtThnaoYPcI+AR8gch36oNAAOdOhjM1OBRFV1qBAn421ChgCGI68oWyI+A0ooqO5fy2dancmXIJkPWGzAVJqAcCTf+deYQfu3SKG55MIRQAAAABJRU5ErkJggg==)
были неположительны.
Рассмотрим теперь автономное уравнение (1):
![](data:image/png;base64,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)
, (10)
где функция
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAVCAMAAAB44J7gAAAAAXNSR0ICQMB9xQAAAHtQTFRFAgICAgEBAQECIiJOJCRQUCQkTiIiXjZNTDVdQCdATjdfRVp5RFl5X3+YXX2VeVpFeFhDlX1dln1dmKu8mq2+vKuYvayZ2s/D18zAws7Z3OPm5eLb5OHa/f39/v7+8PDt8fHu+Pn5/v397fDw+fn47/Ly8vLv/f3+////g96mGgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABoSURBVCjPjdA5FoAgDARQ3FdcwQUURUW9/wktTSx8pPxFZhJyf4b8wDwrBEtAWghrJPpMv6BqhnZsg7dDOErH9Q1KaSiOPcMRg4wNBp5rBEfFcHWZCADqujmFx3XFlBoIPfGN3T9s4QFuqDBgqsuIaAAAAABJRU5ErkJggg==)
непрерывно дифференцируема при
![](data:image/png;base64,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)
, причем
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAVCAMAAAAtgX2+AAAAAXNSR0ICQMB9xQAAAQtQTFRFAgICAwMDAgEBAQECFhUwLxQULhMTPyY/JCRQIiJNJSVQIiJOUCQkTiIiXjZNQShBTTZeXTVMTDVdQCdAXzdOTjdfRVp5Q1h4RFl5RVl5Xn6XX3+YXX2VeFhDeVpFeVlEa0ZrakVqenpraWmFYICYlX1el35eln1dmIBgmKu8mq2+may9mq29u6uYvq2avayZvKuYva2axrevwMzX2s/D2M3Bwc3Yws7Z2c7C18zAw8/a2M3C3eTn2uHk3OPm2+Ll5uPc5eLb5OHa/fz8/Pz8/v7//f39//7+/v7+8PDt7/Ly8vLv7fDw8fDt+Pn57fDx+Pj3/v39/f3++fn48fHu7vHx9fb27+/s////6ggkIwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAFuSURBVDjL1ZNtU4JAEMe5nlM0s2dT07JSMk3Dh0jzLJIDzEzL9vt/ku6OG8CBxhc1zXQvXFz2t7v/Y1eCHxzpl+An/ZnbgesZfAMZuk7mYVOWStQQM2cJj50bkjCWXCN0S/zwS7yj7o8AGhuU1Z2Dt7phMA2x5aYPJueKkyPP6iLnAE68BtlxpgXQPhi58Nvd5pA/XLAchGki+gSgkgrCeP1B/DjwNLu0HGEl37epD1S00jMaiKrAyQ+eW+iYsD/tKI20Yy2v7ctjR07Uua1Kulrgd8ZiAIpCRyEUtmMat1UB41VF+K8CbXMYr3lwP2nNweNMU8BKoG0ut+9phpvDEbeqA5P6aQoM4nY01/b0pCkASRRSRPvxHhug+zI+m9U7tEDCCl63ejT7lDX3O/d3OuJFsUSgRitMs6jMOiqETUkNIU2MpzEhXoy92/WNpJm3FixGNf2458X4R9KUtUVbpaKIP7/tWwzrb/b5P8FfoE6AUGdj6x8AAAAASUVORK5CYII=)
. Тогда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACcAAAARCAMAAABpXkW3AAAAAXNSR0ICQMB9xQAAAGBQTFRFAgICFBQvLhMTRVp5XX2VXn6XeFhDeVpFenpraWmGYICYmIBgmay9mq2+vq2avayZxrev2s/D2M3Bwc3Y2+Ll3OPm5uPc/f39/v7+/f3++Pn5/v39+Pj39vf3+fn4////JE4gRwAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACESURBVCjPtZHXDoAgDEXr3nvVyf//pWCJYjBRE+0T5Jxy2wDsWcEXXkd16wHV21wUT2PXa1ABwivAqLEEa2BslCNRjwIoN7WzcDtEcqRQvrgD8lozvh5rB+RNbkXXc64CNg9z32F4kXsAEAuVSRvMeaOvewDupbx78SDRhlPBJ//7o7cCXvlHFyIDWjwAAAAASUVORK5CYII=)
является положением равновесия уравнения (10). После замены
![](data:image/png;base64,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)
уравнение (10) принимает вид
![](data:image/png;base64,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)
, где
![](data:image/png;base64,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)
, функция
![](data:image/png;base64,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)
непрерывно дифференцируема при
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
при
![](data:image/png;base64,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)
. (11)
Из (11) и теорем 5 и 6 вытекает следующее утверждение.
Теорема 7. Если все собственные числа матрицы
![](data:image/png;base64,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)
имеют отрицательные вещественные части, то положение равновесия
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAMAAAA11AaTAAAAAXNSR0ICQMB9xQAAAFdQTFRFAgICFBQvLhMTRFl5XX2WX3+YXn6XeFhDeVlEenpraWmGmay9mq2+vq2avayZxrev2s/D2M3Bwc3Y2+Ll3OPm5uPc/f39/v7++Pn5+Pj39vf3+fn4////sZ+1HQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABZSURBVCjPlc5JDoAgFAPQ74AjiKhQB+5/TmMQAoks7O4lTVqyaejLxiWYXHJ9PFUYeM9UrFBU7aEv6onFe7ock/2jXWJD9o2FN4ziejjl9loQs1dHPP//h2/YFxiIaYU5eAAAAABJRU5ErkJggg==)
асимптотически устойчиво; если же хоть одно из собственных чисел имеет положительную вещественную часть, то оно неустойчиво.
Пример. Рассмотрим систему двух уравнений
![](data:image/png;base64,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)
Координаты положений равновесия определяются из уравнений
![](data:image/png;base64,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)
. Положения равновесия:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK8AAAAtCAMAAADvNMuUAAAAAXNSR0ICQMB9xQAAAd1QTFRFAAAAAgICAQEBAwICAgEBAwMDAAABAQECFhYxFBQvFRQvMBUVMRYWLxQVLxQULhMTPyY/JSVQJCRQIyNPIiJOUCUlUCQkTSIiTiIiTyMkTDVdXTVMQShBXjZNTTZeQCdAXzdOQ1h4RVp5RFl5Qld2RVl5Xn6XX3+YXX2VeVlEd1hEdldCeFhDeFhEeVpFaURpa0ZrakVqenpraWmGamqHaWmFYH+XYICYeI6umH9fl35elX1dm3pomXdimnhjh2pqkXiFkHeEhHeQjnaDkXmGhXiRmIBgg4+lhJClmZmtgo6kmpqumay9mq2+mq29l6q6mKu8lqrGpY+DpI6CrZmZrZqapZulpJqkvayZva2au6uYvKuYvq2av7+vtra9sLjHr7fGp7rNubnArrbFxqqWxbauxrevx7iw2M3Bws3Yw8/a2s/D39bSzsHB0NDQwMzX09zcwc3Yws7Z2c7C18zA09fg2+Ll3eTn3OPm2uHk4djU5eLb5+Td5uPc5OHa4+DZ/v7+/Pz9/fz8/v397/Ly8vLv/v7///7++fn4/Pz89/j4+Pn5+Pj37O/v/f39/f3+8PDt9/f26uzn7fDw9vf48fDt7fDx4ODn8fHu7vHx9vb19fb26enp7+/s////FBI1sQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAARySURBVFjD7Zn7VxNHFMeDMta3lkpQtLSUlodPfGKxpVRtWmuIBV/B+H7gmqiYQENosnQadsnGQKEPWip1/lZ3NjOzs2GCm2T2ePR4f8jZ3eze/cyd79x756wPvV3me0d54W9SX5uF3vJOKx9qEnH1xkczXvLmvuyRPK+B4Ix3vDAclS7E4SD0jDf9vQcrZyjpFa/RT7UL80WDEngzR597xJu+RXEVUAfAGrB+4o0F2A3vgxQNyQ/GlYJ+SFKmiAW94TW+tQEx7+mCHN6qHDl5p0VJRj/nOFaPSuLl41Adr9E1IJLvbftY/VEeL7qYrJEXPU4Klv79k/axEsS8UA7vV3dq5b10Q7D07w+yw9m9UZRpnnsiZ8V9PVirHm4+FdzC8cZwFxEAIXL6u9m40GSczYu0Pz2Pb+ItZ2fvUl6xCzTN53yLl1QBlN4UXJ3XYXChW1vwg7Wj2JPuXyPQ/h/7Wv/s/ouXD7wGwCgU8ur+etHyMfYDAOp9G1I2LygaGnl25W/3vEqDNmtWvuH6uPW23SkuJISgcW1rIbNn0vmQ7o+L46t/nBKlp24Nze5bNyDQw2Ut0OOad/Gwhn6ZwONvt7IIlzbsTBVuLaBMyz9csBIIjbUWK3FfiWPehVX5rZ5b/xehcd9Hms0LsThgfr6MxMcSwsu9dPJ6O/BvpAO/YkbAi6632/lwe4r84D9LHHMu4NRmc8Jpz73URMNr8cbAxmROAZ8VVmjcGoOYd4nOv3EgagUuqm4BZCWW8KrN/7Gx7zD/0XcmRLxm7JmLMR4GRVh4iR6ud4adQggQSfeU5bXebM3iMew63awtnKdDfXFmrjjUIq++M+6GN91CXSDj6jLTgyO8hFfdukrvwXjzzPDLCG9uyMrYkc6pZo0NtZ4MlfIGHbzqNiFvuPNX4gLpu6xoET1EfA2ak3d2f1yY85x6AMxsXrz1gGZ+6q2r26GJ1xvPa0k3LdZvL2Au9NNcb7zU9AFW3P82Lxw50o5ysCI9xCzfcPxCPj/1M1azuj2JYBletp0yuszARNoKAl7s4hPiwvhmklcvvn/xHOXN5ZWQenx5ZKKi/KDvNruV3LjPNHMxKG0Fo+vCi7slvNlTny9DLExItRj7Yvmln+CHE+wyzsy8i1jDHNXvYpNv1Dw+FaS8w2YUjYOsyLrNv4GfoPkomYRACPuhzYdxViP1AoD1KRTpQZnNVILmI1FWj+3LzAXJOjGmXzrVoZX14vW8Wbv6659OuuvTFszCgrKPV06fWd9El1e1ynhZu4DNWWjL4+Lp1xsFhbNvUHi5Vl5bv1y7YEW420VfucpN4QSq2Cri5doFGeYVr7OWFNsFGTaS8oRXvc2fFdsFKXbRG15+f0zbBRlW+/64jN9+zi9pF2TY0ncFT3jRQ3vfTdsFGaYMIG941XsMl7QLcuQ74RGv0U82NKxdkCKH88gjXhQ7UZQAaxckGKwqvC6/BwzHJWnWxlVCyDteFIhL/j6kVDlLbr9nBSR/H6pWVO/q98L3vNXZK8dG6G5/f+YBAAAAAElFTkSuQmCC)
Соответствующие матрицы
![](data:image/png;base64,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)
имеют вид
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVMAAAA9CAMAAAAnHHrYAAAAAXNSR0ICQMB9xQAAAeZQTFRFAAAAAgICAQEBAwICAwMDFRUwFBQvExMuLhMTLxQUMBUVMRYWPyY/JCRQIyNPIiJOJCNPJCRPUCQkTyMjTiIiXjZNTDVdQCdATTZeXTVMQShBTjdfXk02Q1h4RFl5Q1h3RFl4X3+YXn6XXX2WXn6WX3+XXX2VX36Wd1hDeFhDeVlEelpFeVpFakVqa0ZrenpramqHaWmGd4SQYICYeI6umH9fl35eln5el39fm3pomXdimnhjh2pqiGtrkHeEhHeQj3aDhXiRkXiFhnmSknmGmIBgg4+lmZmtmpqugo6jmay9mKu8mq2+mq29mqSkmay8lqrGpY+DrZmZpI6CrpqapI+DpZulppymvayZva2avKuYvq2arqWPsKWQuLi/v7+vt7e+r7+/oaGmv7i4vre3r7fGp7rNubnAucC5uMXMxqqWxrevyry5wLm5x7iwxLauwMCw2M3Bwc3Yw8/aws7Z2c7C2s/D39bS0NDQ09zczcDAz8LC0tbfwMzXytXPwcHOz9XK3NzTzsHB09fg3+bf2+Ll3OPm2uHk4NfT5eLb5+Td5uPc5OHa/f39/v7+7/Ly8vLv/v7/9/f2+Pn5+fn49/j48fHu8fHz7vHx7fDw8PDt9vf3+Pj35uvp/Pz89vf4/v39////SrTBjQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAdRSURBVHja7Vv9f9NEGG8iwzkRpB0IKEg3hlIYitrhG5MXO7UbwmBix/AF32WitrRVQASVZXYx10Cz2m0Vvf/Uu0vSXJJLlyvJxw7z/NB1ueS+vW+e57nnee4uBiMJWmIRBRGnEadrRZRu5BQocC2KAvS/Iug+TkH+seoapFSNF0C3cgrSyTVq9JnsnS7lNHeFx0soQQ6AhcDT/3QWdCWnlTGOAZ8XhEKopN59dmeN4/bJubA4bWlPB1qkjXL40vzGqpoohEipGhe5OF14fjEcTkFaEAZwv/WEOM7bh/w5B//7ihCWuAbNLTm+7rGihsFpGjnEdBZRukUq7+Id8KzEwf8GyfjoGk7L2VA41f7EH+dqYGSCvwsu0y9tQjer/cUu4lR9oxaOP1WQHz3TyG9a4u9CfYvj5i7kVBtthMEpWE6g2fibp0Sxg9C9wuFOdU7l3m7iFJ6dC4PTvIj86eQLtZGk131tYr5LL3HgdaE/ha98EQKnaj92o9qH3jappbwd7aXTPIaWQnHU+V3dNO/DV0+HwCkxSFj5rbLV0/J/kJRAOIXlXSvLiSswRFEOP73y33NKXmzz/Vob/TnzUY8UCKdwRhBCpVSNC0IPl28JhdPy+nlleYuk7bMbOIWjffyj40rHnHafhMIp1h004VdsUwdYHq7iEAsLlB/JYhUYXoo49cspJBP7+STdQiqigi5w9uo5lBVD+Ym5iFP/nOYGK9voGao+TP83VdUrpPK2RsSpb07Lgj3cJ1kqQGaPPijAmYGIU9+cOkTdLhGi18+BvECFA7IebgHD0YKIU/+c6iEr0svBXNLGtZ4WpA1Hm4w4ZXOqOAVdyxmcyr1Zu/72ZyPb98Gp4BSK0+a+AovTyPY7t30w+9yALdKPbL9zTtXtc1gb8xPyoRW6js8oCUSc+uQUpsdxepWEWkqgM1Z7XvBgcPra6ZDXTVuKuoWRMsHlYXflquRZYLZ1yfer/d0dDECuGO66qSWsPLQeZ5SUPPWULscC1tvwFnZloS1A/WCnACHZvrluaoetwtWutOeUegPe+6nYo2FWFtwAxY4BFnbMh8upuW7aURd+/GndU0u9Vl1ZlYVAARZaAGHNUfq6qSu975RTQDIH1JMCSH8j2dZ1B0JryM4mRmXBB4AbweLU0TRjOrtwONXXTa9970rvO+U0Jwgbq8v9xeX+r1PioFE9gKwCQmvIziZ5aztFtQOAFoDZze6am1PSVGo1tQDCmffNdVNXeu9HSpYOmrmVfGgRXr+diF1MxNZLpYcls3oAHQUE9Mjdo0tmyGEHdy84ugDisYtxFwCc2ZMbYgPYmhCAkSKi+Du8dVN3eu9HzO1SVG4l9w2iYci9RbySL2+QctaQbQj4EdFIx6CxmGAN2flTXjYAhjDAXi8AWzcZA2DI3WQBnJVCXDd1p/d+hLUPRe5DBmkOubdIDZkgUDvVqSlEBzeVilGtsQPsZQM4Eeg5qpmiEEwAfIOLU6B0vk3Wtm7qTu/9CHtiLYtFa8iWaRKEZmpjlTGFEPB6XBj3sH0nQIEF4EKgfp4dQU3oAOoxxn6pzEOiOATug1Nj3ZSR3vsS9wPyT4oyMlHpLfzRWwDoD6keQKuAcHXUxanZ9EnViILlrW1ieAxwGAHcMAHMrM+NQAUWpRYCnp1kY62oNMHa1zf788370lNj3ZSR3nM5VNoykY/EC+2C0PNVn9AjpccNHISwX5igdEc7bhS/kc/DTbp/w8aTbGv6yEfaAYDVzQEawQSA03rTSfR1UqIAMJyLU3X41rs3IUkYiBOw9jZhr+LBthGnBbH3XDu+anjuqB603V4JPsXBDl8uiwDmIR+CmSXU34YMTssvkiStfqyG3tw40Pabzl078HhDO87OnHPryJsNZD9/eWBVM5F3zPkcMcjjjLYe59z6Zwdoj1C6YgEAorMiQKIwtKUKrxNX8bu+twnoGkT2q+N/bQ/JY4AcDgjm3MnM6qceVLrE0Tza8KYUh2HqQe49m/ZHmkeXvBFQHGbeDUrE1Ykg8wyjYqA3Ylcxpe9tQgpOrHJGfyH4IWsk6GIZn2IJ6MxZusB1ji/tnash1y4EsDs1Q2VSDpmmEJSSHrki278wRtTQFkTpsy+4XNP3NgHlsxWFcGpOIRfGACk4kqfQ3eR6UGcj02v0HJ+RDCBOMX/XqloqFovtXDTWOolfwK5C7kOeEk1worD5r9EGMXOTdPnRAtCf+qCAFBtEZ3gNWQfqrxcAiuIQb4Kwe3EdSdjAt3gBKb/nHpi9eu5vqNt+c3QJ6+k/5JTOkRt3LtemjKd+eefeexKMODVl4cnb8ZPwV8vYiAfA7pG4iqlqhmQAl2vYqyzCXDGdBOShU6D5peVwTgU27z8wcq1heQUBW/sRdmW8fmJx2nTJ4Lt5R2vEKSVq/KT5VY+goHqCNdNpb1KTR0bY3Ig49SmTnR7kiDj1EhRBRZwGTGmp41MHEacelOIIKuI0UJm+j3Qu4jR4iTiNOI04/X/Kv2Imqu4fRgY3AAAAAElFTkSuQmCC)
, или
![](data:image/png;base64,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)
.
Собственные числа определяются уравнением
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJQAAAAYCAMAAAArkCRFAAAAAXNSR0ICQMB9xQAAAQVQTFRFAgICAQEBFRUwLxQULhMTMBUVPyY/JCRQIyNPIiJOUCQkTyMjTiIiQCdATTZeXTVMTDVdXjZNQ1h4RFl5Qld3Xn6XXX2WX3+YeVlEd1dCeFhDaURpakVqa0ZramqHl35emH9fln1dkHeEj3aDkXiFgo6kmpqumKu8mq2+may9pI6CrZmZrpqapZulvKuYvayZvq2av7+vv7i4t7e+uLi/sLjHx7iwxrevzca5z8LC39bS0NDQwc3Y2M3Bw8/awcHO09zcws7Z2c7C2s/D3OPm2+Ll4NfT5uPc5eLb/f39/v7+8vLv+fn47/Ly+Pn58PDt9/f27fDw8fHu7vHx9/j49vf3////quUZhQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIOSURBVEjH7ZZZV8IwEIXjvuEGLqhVcN8R9w3QYrHStGxK/v9PsUlLyDTVNn3Cc5wHDqfMd7nN3KZBZAALDbqpet1SYi0r4Z9GgYIpPI0OVaTt7FEyT3b2OLapRwdvOCriT0Y9mav3CJCasvjYTozQ1Q4uvX/h9HLYALgiKPf7AaKmcmjZv3jVCOlsasL6tdbSDay12RSun9kljv8OrkugBBQQKlmeKfOW3DHjVrkScpPlCUfM3VC6QczZmvvdHGHR4LgqKFV50sEzJZ4p/MI8rfBB2Ds9wY4Gc3bhahNz7pOQ+9fzL9LHk4Aw/+s6IVXa5Zn62Hc/igihiqSdCzxiTJsU3YmdOflV0seTgKDMccP/8ExtpwNh4tp43gjTNhfEZRBwNZBGmxWdUHXK/QmndN/Ux+iWAztbu22hU0Q9bcb2iuMSKJIhICF55NWqbKqQedADnUN+5wXtFNGetpBVjkugSIaAsJgpc9Q31UnpQlThFDxtaQqiNsBVwMD4YKYKmYZ9A7c6rl39SVsXFkrAVcDA+OxsiYkxU52U+5yctZsH4UGvAen69lKXxqifV4hHgYGgg3rLdJszFW+fKtJNzhwDO7+912Pz4CXtvrQRbSz0n2mIK4ByFf09KfI8hRdr8sWmFv3mTgzGOeR5rwZQnelKDOnEYJyTJw7eHdbinXBkcDMeOPDH4X9Tf87UNz1qTIjEHygQAAAAAElFTkSuQmCC)
. При k четном
![](data:image/png;base64,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)
, при k нечетном
![](data:image/png;base64,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)
. По теореме 7 при k четном решения
![](data:image/png;base64,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)
асимптотически устойчивы, а при k нечетном неустойчивы.
Предположим теперь, что правая часть уравнения (1) и решение
![](data:image/png;base64,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)
периодичны по t с одним и тем же периодом . Тогда в уравнении (8)
![](data:image/png;base64,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)
,
![](data:image/png;base64,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)
. Далее, так как
![](data:image/png;base64,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)
равномерно непрерывна на компакте
![](data:image/png;base64,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)
, то в силу периодичности
![](data:image/png;base64,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)
выполняется равномерно по
![](data:image/png;base64,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)
. Поскольку
![](data:image/png;base64,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)
— периодическая матрица, то существует замена переменных
![](data:image/png;base64,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)
, (12)
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFcAAAAYCAMAAAC4GJHnAAAAAXNSR0ICQMB9xQAAARRQTFRFAAAAAgICAgEBAQEBAQECExMuFBMuFRUwLhMTMBUVLhMUIiJOJCRQIyNPJCNPUCQkTiIiTyMjTTZeQCdAXDRLRVp5Qld2Q1h4Q1h3X3+YXX2VXn6XXX2WeVlEeFhDd1hEeVpFdldCd1hDaGiFYICYln5fl35emH9fh2pqkHeEmIBgnJGRmZmtmay9mKu8mq2+pY+DrJiYrpqapZulvayZvq2avKuYrq6ux7iw18zA2s/Dw8/a2c7Cws7ZwMzXwc3Y0dHRwsLP3uXe3+bf3OPm2+Ll2uHk5t/f5uPc5eLb5OHa/f39/v7+/v39/f3+9/f2+Pn57fDw8fHu8/Hx+fn47/Ly8vLv9vf39/j48PDt+Pj3////7tJDwQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHRSURBVEjH7ZTZWsIwEEaTVgRXQEUtasUNFS11wQ3crQikbJoWdd7/PUyTli5f9Uq9IjfTTmbOJP8kQfA3A424v8slQMyA9bhtQkgHTD/OcfDxE4s4DJMlQmPuMa2BbwXXJDsYY6V72hvmlDBCzCdN9b/FvqYxLhNSwXkT3i4Ong6Zz7Oca17hHCNWZS2Q1UglDKBrKPEcpg33RPctsDMy1u2sBvZe7VpnTs9y7tVYjUdWbgL5doZxGR1pYe5R3Su8NQCqOrNFBRjsuA/tjrCC20wpIvLS4JqYAW4z5db09zHvgu3s4jvndvcMOLHsdK5XVIQV3OKU5TWK2SrWPW6ddNfxdlTWs/G6qFzFGlXL5GPBGE7VAueMqkusAC1gJE9bQR0QllDeldMkw9HdQLfCe61TVWa9vYs9v3ZmRUQhHSL67kroFty1+UNCWKzrxeI6FFfiudlV/nk+Y0W5MccB4HPTxcI92ytbS2WpF3vfdhNOJ6iqQJQLjQm0+B5JOU8a3tXpUNYyqMSvF+z0bJ+Q1mTNVZKL126lEvUOVCVUDl+55py7LVqQ8x8PTreWB9+8DyVHtlzPVVIPuphNGqHz6/+dYd7oxkQ4YvT+jrj/xf0C+Tib1w3c2dgAAAAASUVORK5CYII=)
— периодическая с периодом функция класса
![](data:image/png;base64,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)
, причем
![](data:image/png;base64,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)
, переводящая уравнение
![](data:image/png;base64,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)
в
![](data:image/png;base64,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)
с постоянной матрицей коэффициентов
![](data:image/png;base64,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)
, определяемой теоремой Флоке. Следовательно, замена (12) переводит (8) в уравнение
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAVCAMAAABsdQABAAAAAXNSR0ICQMB9xQAAAN5QTFRFAAAAAQEBAgICExMuFRUwFBQvMBUVLhMTLxQUPyY/IiJOJCRQIyNPTiIiUCQkQCdATTZeXTVMTDVdXjZNRFl5XX2WXn6XX3+YeVlEeFhDakVqa0ZrmH9fl35eln1dkHeEj3aDg3aPkXiFmay9mq2+mKu8rpqappymvq2avKuYvayZr7fG2c7Cws7Z2M3B2s/Dw8/awc3Y39bS3OPm2+Ll2uHk5d7e5eLb5uPc5OHa/v7+/f399/f2+Pn58PDt7/Ly8vLv7fDw+fn48fHu7vHx7Orn5+rs9vf35ero////CBodFgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAHUSURBVEjH7ZVZc4IwEIAhPaXVVqsiFnsotmgRtWiliUrEXvz/P9SQcCQCT850fOi+OCa7++2VRQr+RqSD4EBEBBZeR5dUIV8LihyI8h3psgTkRhFocQpAE6Hl8yqA67aXo4HbG4FjHTn5rjqKZ0mjghifiGsTgGNia194QV5W7tWM54zBpICjBrjcE478+2zk2yibxcvujXv9kXJoG/IwuDwKFmeGoMBz6DnpUceg/95LcyhckV+zmXD8FgDyiZMaJr23lM1Sq684BYEDbXIuAQNXHdZNOalLYuLWvJjz+RVAnSnogInKtAeyLKm8Aolj+bCJ47CJo7C1lsLQLC0qiUlYknTe9Nz++JoRueDjkOM4fI10ziYKQ6a0rfLTFJlE7ZVEjFi3RcnB5elOHGnd/FYDLTWCjDiD+iqD4TmcF7FuoaHe2EmX6497zjRZ0iR7mMFwdYN3U4TessMK1+U+JPWfI0GB42wfv6lnXA1fiVv76XoBm8vUZzoHJtd4Xkx6jCvCZBBON+bAIQA9WmK9Tx8hebHu6aUX8D4H6r57FIbjZcrh+8A3s2TnvQqrJd5He3DGChlwZKvCfsEVoTLbymT/74LO1RPn79Fb76C+P/+cIvkFP8UmJapzHa8AAAAASUVORK5CYII=)
, (13)
причем функция
![](data:image/png;base64,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)
определена и непрерывна в области вида
![](data:image/png;base64,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)
. Условие (9) также выполняется. Действительно,
![](data:image/png;base64,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)
в силу (9), ограниченности
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
и поскольку
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAbCAMAAADmgEdDAAAAAXNSR0ICQMB9xQAAAJlQTFRFAAAAAgICAgEBFRUwFBMuLhMTPyY/IyNPIiJOTyMjTiIiQCdATTZeQ1h4RFl5eFhDeVlEdldCd1hDYICYmH9flX1dpY+DvKuYvq2awc3Y2M3Bws7Z2c7Cw8/awMzX2s/D2uHk3OPm5d7e5uPc5eLb/f39/v7+7/Ly8vLv+fn4+Pn5/v397Orn5+rs9/f2+Pj39vf38PDt////zJv/eAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADfSURBVDjLzdRZD4IwDADg1RsPvAVUQIQN8Lb//8c5YWN7WAzGaOwS0j18WdstEHw/yA8N5UsGRW3zwhDtNFLj6G8bRil70zAHwGN1DKuydTfNLK+OWe1Eko83iNvRQTNHysNg4oFAcScSH2nyCUCjGRn6cVu7or5tL0XM+htlTmc8LvzqHEaruExJwIwGSyJNCCoaBHxp4rZuSmKo7TorSNlKovcjiME4vMtibhM+Z8dWc2PLgNJ9ajDJMBVZaN/ulq/ux30WPjfeT6QmCOD/67v+1ABfMgC1zR/8d35hHhYV7dWxdbY5AAAAAElFTkSuQmCC)
эквивалентно
![](data:image/png;base64,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)
. При этом, как отмечалось, имеет место равномерность по t.
Согласно лемме из п. 2.1. вопрос об устойчивости тривиального решения уравнения (8) эквивалентен вопросу об устойчивости тривиального решения уравнения (13). Так как
![](data:image/png;base64,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)
, где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAYCAMAAADNlS1EAAAAAXNSR0ICQMB9xQAAAKVQTFRFAwMDFRUwLxQVMBUVJCRQTiIjTiIiQ1h4RFl5X3+YeVlEamqHYICYmH9fln1dmIBggo6kmpqumq2+may9rpqarZmZpZulvKuYva2auLi/v7+vt7e+sLjHx7iwxrevzse6wcHOws7Zw8/a39bS0NDQ09zc3OPm3eTn5uPc5eLb/v39/f39/f3+/v7+8vLv+Pn57/Ly8fHu+fn47fDw8PDt9/j4////aFtBtAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACJSURBVCjPYzDDAhgoF9TS1sEQ1OVl4MQQ1JAxk1XDYqaeAhZBTQFMQV0+dn0MQU0mbgMMQXEOeUV0QUNWJahNWrpwQXEOfSNJoMlmRlxCMEFDNiBTxNhE0MxMWU0bKijBArRFg5lR3cxMVApEogaIkbQKZihpMgtjCsqpipliCIoY8PNQKTowAADad13COmb5+wAAAABJRU5ErkJggg==)
— собственные числа матрицы
![](data:image/png;base64,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)
, а
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAYCAMAAADNlS1EAAAAAXNSR0ICQMB9xQAAAIRQTFRFAgEBAgICFRUwMBUVIiJOXTVMXDRLXzdOQUEoXn6XXX2WeVlEYICYl35ekHeEmIBgmq2+may9pI6CrZmZrpqapZulv7+vt7e+xrevwMzXzsHB39bS0NDQ09zc3OPm5uPc/v39/f3+/f398vLv/v7+8PDt+fn47fDw9/f27/Ly9/j4////FNc6OAAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABuSURBVCjPY9DGAhgGXFBBEUgooQnycmprK7PK0UhQQQUhyKWtrcomp6Ktxi2AEGRR1+BmkJTS1JaWU4IJCnEwMsnxMwJVCYsxyUEE1fg0oRaoicvAtCMslmcWhAuywwQlZEW1MAJERJOfh1aBDABhRklwI5Y99AAAAABJRU5ErkJggg==)
— мультипликаторы линейного уравнения
![](data:image/png;base64,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)
, называемые также мультипликаторами периодического решения
![](data:image/png;base64,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)
, то из теорем 5 и 6 вытекает следующая теорема: