16 problems

Previous-visits conjecture. To predict the next step in a time series, a good indication should come from the previous visits the system had made to the phase-space neighborhood co…

Consider $C^1$ families of vector fields $\dot{s}=F_\omega(s)$ whose parameter $\omega$ varies in a smooth, connected, $k$-dimensional manifold, typically $\mathbb{R}^k$, with…

Nonchaoticity conjecture. The map is not chaotic in the sense of Devaney, since it has the same set of fixed points and similar sets of periodic points as the corresponding map wit…

Consider the asymmetrically electrically coupled pair of Rulkov 1 neurons with $\beta^c_1=\sigma^c_1=\beta^c_2=\sigma^c_2=1$, $\sigma_1=\sigma_2=-0.5$, $\alpha_1=\alpha_2=4.5$,…

Let $C_{\mathrm{bs}}$ denote the boundary associated with the transition between bursting and spiking in the coupled Rulkov neuron parameter space. Chaotic spiking-bursting conject…

A fractional ordered dynamical system (FODS) is a dynamical system involving differential operators of non-integer order; here, "order" refers to the fractional differentiation ord…

Multifractal-label conjecture. The observed feature reflects the multifractal property of the chaotic system, with each monofractal labelled by $s\in\mathscr{S}$.

Spectral-invariant conjecture. The geometrical and dynamical information of $\mu_{m}$ can be extracted from this spectrum.

Mixed-beta conjecture. The probability density function of $r_{ij}$ can be described by a superposition of incomplete beta distributions,

Black hole radiation behaves as black-body radiation with finite temperature and resembles a thermodynamic system characterised by entropy and other thermodynamic quantities. Maxim…

Let a many-body chaotic system be deterministic or nondeterministic, and consider its Lyapunov exponents at late time. Here, RMT denotes Random Matrix Theory. Universality conjectu…

Bifurcation-cascade conjecture. Systems with more states, perhaps infinitely many, can present a cascade of bifurcations, leading to aperiodicity and chaos.

Balibrea–Guirao–Oprocha conjecture. There exists a weakly mixing system with a fixed point but without invariant $\delta$-scrambled sets.

Rough-dependence conjecture. High-Reynolds-number violent turbulence is caused by rough dependence on initial data rather than by the sensitive dependence on initial data associate…

Let $S^2$ be the two-dimensional simplex, and let $W_\alpha:S^2\to S^2$ be the quadratic stochastic operator defined in the source by equation $W_\alpha$. Assume…

Let $f_t$ be the flow of the Lorenz oscillator, and call a set $A$ attracting if it has a neighborhood $U$ such that … A strange attractor is an attracting set with the irregular p…