Related papers: Symmetric and Asymmetric Tendencies in Stable Comp…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
We study the probability of stability of a large complex system of size $N$ within the framework of a generalized May model, which assumes a linear dynamics of each population size $n_i$ (with respect to its equilibrium value): $…
We study the dynamics of a rigid body in a central gravitational field modeled as a Hamiltonian system with continuous rotational symmetries following the geometrical framework of Wang et al. Novelties of our work are the use the Reduced…
We show that a large effective number of commodities can be a source of equilibrium stability and uniqueness: expanding substitution opportunities strengthens aggregate substitution effects. We study finite dated-commodity exchange…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of…
We study the problem of robust performance of quantum systems under structured uncertainties. A specific feature of closed (Hamiltonian) quantum systems is that their poles lie on the imaginary axis and that neither a coherent controller…
Forty years ago, Robert May questioned a central belief in ecology by proving that sufficiently large or complex ecological networks have probability of persisting close to zero. To prove this point, he analyzed large networks in which…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Over fifty years ago, Robert May applied random matrix theory to show that as ecological systems grow in size, stability decreases. What emerged from this and the critique that followed was decades of what has been called the…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological…
An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…