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Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…
Two zero-range-interacting atoms in a circular, transversely harmonic waveguide are used as a test-bench for a quantitative description of the crossover between integrability and chaos in a quantum system with no selection rules. For such…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schr\"odinger equation, we find that the…
We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…
The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an…
Control of cooling and heating processes is essential in many industrial and biological processes. In fact, the time evolution of an observable quantity may differ according to the previous history of the system. For example, a system that…
We propose a new criterion to analyse the order of phase transitions within a finite size scaling analysis. It refers to response functions like order parameter susceptibilities and the specific heat and states different monotony behaviour…
The properties of interfaces in non-equilibrium situations are studied by constructing a density matrix with a space-dependent temperature. The temperature gradient gives rise to new terms in the equation for the order parameter. Surface…
We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing to define a temperature T_{th} along the same lines as in the…
We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is…
The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits…
We study the thermodynamic properties induced by non-reciprocal interactions between stochastic degrees of freedom in time- and space-continuous systems. We show that, under fairly general conditions, non-reciprocal coupling alone implies a…
The effects of quantum and thermal corrections on the dynamics of a damped nonlinearly kicked harmonic oscillator are studied. This is done via the Quantum Langevin Equation formalism working on a truncated moment expansion of the density…
There are insights of chaotic properties in economic systems and data. To prove the existence of chaotic dynamics, the establishment of a deterministic model is mandatory. A global modelling tool (GPoM) is used to search for mathematical…
We present a simple model that recalls two different patterns depending on the temperature. To realize a change in recall pattern due to temperature change, we embed two patterns to different graphs: the first pattern into a fully connected…
We study transient thermal processes in infinite harmonic crystals with complex (polyatomic) lattice. Initially particles have zero displacements and random velocities such that distribution of temperature is spatially uniform. Initial…
The systematic approach for the off-perturbative calculations in disordered systems is developed. The proposed scheme is applied for the random temperature and the random field ferromagnetic Ising models. It is shown that away from the…
The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates…