10 problems

Let the non-smooth system be the system denoted by … g(x,y,varepsilon)=alphai h'(x)+varepsilon y quadtext{if }xin(ai,a{i+1}],quad i=0,1,ldots,n, … with this function $g$ has no lim…

Consider the piecewise glacial cycles system … exhibits a boundary equilibrium bifurcation. The claim concerns parameter-driven changes in the type of equilibrium, but the supplied…

Let $m\geq 6$ be even, let $f(x)$ be a polynomial of degree $n$, and consider the discontinuous system … where the zero set of $\operatorname{sgn}(g_m(x,y))$ is the union of $m/2$…

Let $H(n)$ denote the upper bound for the number of limit cycles bifurcating from the period annulus around the origin, over all polynomial perturbations $p^{\pm}(x,y)$ and…

Let a piecewise smooth system possess a singular cycle connecting a saddle periodic orbit and a saddle equilibrium, of either type studied in the paper: one involving a saddle equi…

The regularized fold-fold system has locally unique periodic orbits near the Hopf bifurcation and near the Canard curve. Periodic-orbit continuation conjecture. The “small” curves…

Let $Z$ be a piecewise vector field in $\mega^r$ admitting a sliding Shilnikov orbit $\Gamma$. For every $s\geq r$, let $\mathcal{U}\subset\mega^r$ be a neighbourhood of $Z$. Smoot…

Consider the regularized planar piecewise smooth system in case $VI_3^\epsilon$, with the two families of periodic orbits obtained respectively in Proposition and Proposition. Peri…

Let $x(t)$ denote the displacement from the switching manifold in the stochastic system, with switching functions $\phi$ and $\psi$, and let $y(t)$ denote displacement along the sw…

Mode-wise contraction conjecture. For certain classes of piecewise-smooth systems, contraction of each individual mode should be sufficient to guarantee convergence of all system t…