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Isochronicity and Bifurcation of Limit Cycles for Planar Polynomial Autonomous Differential Systems

Author: WuYuSen
Tutor: LiuYiRong
School: Central South University
Course: Applied Mathematics
Keywords: Planar polynomial differential systems Proposed resolution system The high-order odd Infinity Three nilpotent singularity The amount of focus Singular point value The amount of nodes Generalized periodic constant Proposed Lyapunov constant Limit cycle Generalized Center Generalized Centre,
CLC: O174.14
Type: PhD thesis
Year: 2010
Downloads: 80
Quote: 1
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Planar polynomial differential autonomous system main research Benpian doctoral thesis when and limit cycles, the text of which is from seven chapters of the first chapter of a comprehensive overview of planar polynomial differential autonomous system bifurcation of limit cycles, the center plot, etc. the historical background and Research Centre, and can be linearized, and a brief introduction about the characteristics of the work of this article second of a class of seven polynomial system with two small parameters and nine parameters of the high singularity and infinity center conditions and limit cycle branch of the origin of the system is the high-order singular point, no real singularity in the equatorial ring first on a personal computer with a computer algebra system Mathematica deduce the high-order odd point of the first nine months of the singular point value and infinity 7 odd amount of points, and then discuss the system high-order singular point and the center of the point at infinity criterion. Finally, in the high-order singular point and infinity simultaneous perturbation obtained under this system {(8), 3} and {(3), 6} the limits of the ring distribution. third chapter of the center of the singularity of a class of seven polynomial systems, intends center conditions and bifurcation of limit cycles. homeomorphic transformation and re-transformation first system of higher critical point as the primary origin of the complex domain, and then the new system is obtained at the origin of the first 45 odd amount of points, which lead to high times singularity and order fine focus given on the basis of the seven systems in the instance of the Higher Order Singular dotted expenditure limit cycles. Finally, a new algorithm to find the high-order singular point is the center cycle constant has been a necessary condition for the high-order singularity Isochronous Center, and effective way to testify to the adequacy of these conditions. fourth chapter have:-m type 5: -m rational the resonance singularities of Lotka-Volterra system can be linearized to calculate the generalized period constants are looking for an effective method of rational resonance ratio system can be linearized conditions through a new Recursion to find a necessary condition for linear, this method without solving system integrable. Finally, through a variety of ways to prove the adequacy of these conditions. In the fifth chapter, we study the polynomial p: -q-linear resonance singularities. First of all, we transformed by a homeomorphism singularity into the origin. further, we derive a recursive algorithm to calculate the so-called generalized periodic constant. This algorithm, linear recurrence formula, just the right end of the system coefficient as a symbol for limited times, subtraction, multiplication, addition to the four arithmetic operations, avoiding the complex integral and trigonometric functions usually required for the calculation, which is easier to achieve on a personal computer Finally, the application of this algorithm, we study a class of seven polynomial system degenerate singular point Isochronous Center and 4: -5 type Lotka-Volterra system linearization in the sixth chapter, we when the real plane intends three analytical systems such as the central issue of the techniques used is homeomorphic transformation to be three times the resolution system conversion resolution system to deal with the use of computer algebra system Mathematica, we calculated the new system origin cycle of constant and has been a necessary condition for isochronous centers through a variety of methods. Finally, we prove the adequacy of these conditions. has three system origin isochronous center conditions is a special case of the results in this chapter in Chapter VII, We studied a class of cubic Lyapunov system the central issue of the three nilpotent singularities and limit cycles, we apply computer algebra system Mathematica deduce the origin of the system 7 quasi-Lyapunov constants, and on this basis, we get to the starting point necessary and sufficient condition for the center, and a three the nilpotent singularity expenditure limit three ring system instance.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Polynomial theory
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