Sajjad Bakrani

• PhD
• Research Assistant at Imperial College London

We consider a $\mathbb{Z}_{2}$-equivariant 4-dimensional system of ODEs with a smooth first integral $H$ and a saddle equilibrium state $O$. We assume that there exists a transverse homoclinic orbit $\Gamma$ to $O$ that approaches $O$ along the nonleading directions. Suppose $H(O) = c$. In \cite{Bakrani2022JDE}, the dynamics near $\Gamma$ in the le...

Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that t...

Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that t...

We consider a Z2-equivariant flow in R4 with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit Γ. We provide criteria for the existence of stable and unstable invariant manifolds of Γ. We prove that if these manifolds intersect transversely, creating a so-called super-homoclinic, then in any neighborhood of this...

We consider a \(\mathbb{Z}_2\)-equivariant flow in \(\mathbb{R}^{4}\) with an integral of motion and a hyperbolic equilibrium with a transverse homoclinic orbit \(\Gamma\). We provide criteria for the existence of stable and unstable invariant manifolds of \(\Gamma\). We prove that if these manifolds intersect transversely, creating a so-called sup...