Displaying similar documents to “Long-term global climate dynamics: a Hopf bifurcation causing recurrent ice ages.”

Dynamics of systems with Preisach memory near equilibria

Stephen McCarthy, Dmitrii Rachinskii (2014)

Mathematica Bohemica

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We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can...

Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order

Jolanta Przybycin (1992)

Annales Polonici Mathematici

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This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained...

Parameter influence on passive dynamic walking of a robot with flat feet

Xiangze Lin, Haibo Du, Shihua Li (2013)

Kybernetika

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The biped robot with flat feet and fixed ankles walking down a slope is a typical impulsive dynamic system. Steady passive gaits for such mechanism can be induced on certain shallow slopes without actuation. The steady gaits can be described by using stable non-smooth limit cycles in phase plane. In this paper, it is shown that the robot gaits are affected by three parameters, namely the ground slope, the length of the foot, and the mass ratio of the robot. As the ground slope is gradually...