相关论文: Low-dimensional chaos induced by frustration in a …

We previously reported the chaos induced by the frustration of interaction in a non-monotonic sequential associative memory model, and showed the chaotic behaviors at absolute zero. We have now analyzed bifurcation in a stochastic system,…

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors…

This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…

We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…

Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…

It is shown how the macroscopic non-equilibrium dynamics of a class of systems whose microscopic stochastic dynamics involves disordered and frustrated but range-free interactions can be well described by closed deterministic flow…

This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…

We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity in the context of theoretical ecology by analyzing a…

A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…

We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…

This article aims at revisiting, with the aid of simple and neat numerical examples, some of the basic features of macroscopic irreversibility, and, thus, of the mechanical foundation of the second principle of thermodynamics as drawn by…

We characterize the macroscopic attractor of infinite populations of noisy maps subjected to global and strong coupling by using an expansion in order parameters. We show that for any noise amplitude there exists a large region of strong…

Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…

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…

We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…

We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…

Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world…

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…