Related papers: Cycles and Stability
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
In this paper we survey many of the known results about Morse boundaries and stability.
Here we give a necessary and sufficient condition for the convergence to a random max infinitely divisible law from that of a random maximum. We then discuss random max-stable laws, their domain of max-attraction and the associated extremal…
Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases,…
Computer-based attempts to construct lower bounds for small Ramsey numbers are discussed. A systematic review of cyclic Ramsey graphs is attempted. Many known lower bounds are reproduced. Several new bounds are reported.
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
In this talk I will introduce the principle of stochastic stability and discussing its consequences both at equilibrium and off-equilibrium.
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
We take advantage of a rigidity result for the equation satisfied by an extremal function associated with a special case of the Caffarelli-Kohn-Nirenberg inequalities to get a symmetry result for a larger set of inequali-ties. The main…
This paper focuses at the various stability results of reciprocal-nonic and reciprocal-decic functional equations in non-Archimedes fields and illustrations of the proper examples for their non-stabilities.
In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…
We obtain some results related to Romanoff's theorem.
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with…
This paper provides sufficient conditions for global asymptotic stability and global exponential stability, which can be applied to nonlinear, large-scale, uncertain discrete-time systems. The conditions are derived by means of vector…
In this work we argue about the Lesche stability of some systems, that are motivated by the use of fractional derivatives.
In this article we present three robust instability mechanisms for linear and nonlinear inverse problems. All of these are based on strong compression properties (in the sense of singular value or entropy number bounds) which we deduce…
We investigate the typical cycle lengths, the total number of cycles, and the number of finite cycles in random permutations whose probability involves cycle weights. Typical cycle lengths and total number of cycles depend strongly on the…
We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\o}lner sequences of non-empty…
Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…