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Necessary and sufficient conditions on the existence and stability of the fixed points of this system are established. By applying the center manifold theorem and bifurcation theory, we show that the system has the fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation under certain conditions. Numerical simulations are presented to not only show the consistence between examples and our theoretical analysis, but also exhibit complexity and interesting dynamical behaviors, including period, , , , , , and orbits, quasi-periodic orbits, chaotic behaviors which appear and disappear suddenly, coexisting chaotic attractors.
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Google Scholar  C. Google Scholar  E. Google Scholar  H. Google Scholar  C. Google Scholar  S. Google Scholar  S. Google Scholar  Y. Google Scholar  Z. Google Scholar show all references. The stability region and bifurcation region of system 2 in the b , a -plane. Figure Options. Download full-size image Download as PowerPoint slide.
Bifurcation diagrams of system 2 in the threedimensional a , b , x space. A - H phase portraits for various values of a corresponding to Figure 4 A. Article outline. Figures and Tables. Citation Only. Citation and Abstract. Export Close. Send Email Close.
Applied nonlinear dynamics of non-smooth mechanical systems. This paper introduces practically important concept of local non-smoothness where any dynamical system can be considered as smooth in a finite size subspace of global hyperspace W. Global solution is generated by matching local solutions obtained by standard methods. If the dynamical system is linear in all subspaces then an implicit global analytical solution can be given, as the times when non-smoothness occurs have to be determined first. This leads to the necessity of solving a set of nonlinear algebraic equations. To illustrate the non-smooth dynamical systems and the methodology of solving them, three mechanical engineering problems have been studied.
This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos. The author has.
Haller, D. Oettinger, J. Ault, H.
Juries , Memberships , Administrative Activities , Conferences. Curriculum vitae in pdf format can be found here: CV. Marital status: Married, one child.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages.
Wiggins S. Springer, This volume is intended for advanced undergraduate or first-year graduate students as an introduction to applied nonlinear dynamics and chaos.
Росио покачала головой: - Не могу. - Почему? - рассердился Беккер. - У меня его уже нет, - сказала она виноватым тоном. - Я его продала. ГЛАВА 33 Токуген Нуматака смотрел в окно и ходил по кабинету взад-вперед как зверь в клетке. Человек, с которым он вступил в контакт, Северная Дакота, не звонил. Проклятые американцы.
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