Two-Dimensional Crossing-Variable Cubic Nonlinear Systems, (Hardcover)

<p>This book is the fourth of 15 related monographs presents systematically a theory of crossing-cubic nonlinear systems. In this treatment, at least one vector field is crossing-cubic, and the other vector field can be constant, crossing-linear, crossing-quadratic, and crossing-cubic. For constant vector fields, the dynamical systems possess 1-dimensional flows, such as parabola and inflection flows plus third-order parabola flows. For crossing-linear and crossing-cubic systems, the dynamical systems possess saddle and center equilibriums, parabola-saddles, third-order centers and saddles (i.e, (3rd UP+: UP+)-saddle and (3rdUP-: UP-)-saddle) and third-order centers (i.e., (3rd DP+: DP-)-center, (3rd DP-, DP+)-center) . For crossing-quadratic and crossing-cubic systems, in addition to the first and third-order saddles and centers plus parabola-saddles, there are (3:2)parabola-saddle and double-inflection saddles, and for the two crossing-cubic systems, (3:3)-saddles and centers exist. Finally, the homoclinic orbits with centers can be formed, and the corresponding homoclinic networks of centers and saddles exist.</p> <p>Readers will learn new concepts, theory, phenomena, and analytic techniques, including</p> <p>- Constant and crossing-cubic systems</p> <p>- Crossing-linear and crossing-cubic systems</p> <p>- Crossing-quadratic and crossing-cubic systems</p> <p>- Crossing-cubic and crossing-cubic systems</p> <p>- Appearing and switching bifurcations</p> <p>- Third-order centers and saddles</p> <p>- Parabola-saddles and inflection-saddles</p> <p>- Homoclinic-orbit network with centers</p> <p>- Appearing bifurcations</p> <p> </p>

• Two-Dimensional Crossing-Variable Cubic Nonlinear Systems, (Hardcover)
• Author: Springer
• ISBN: 9783031628092
• Format: Hardcover
• Publication Date: 2025-02-12
• Page Count: 386