9 papers
Lie symmetry analysis of a 2+1-dimensional flux limited Keller Segel system
Ahmed Abbas Jaber AlFuraiji, Ghorbanali Haghighatdoost, Mustafa Bazghandi
We investigate a two dimensional flux limited Keller Segel FLKS system using classical Lie symmetry analysis. The complete Lie point symmetry algebra is determined and shown to con…
Similarity Solutions for the Flux limited Keller Segel System with Time Varying Chemical Decay Rate
Ahmed Abbas Jaber Al Furaiji, Ghorbanali Haghighatdoost, Mustafa Bazghandi
We investigate a one dimensional flux limited Keller Segel system (FLKS) in which the chemical decay rate is allowed to vary explicitly in time, a feature motivated by enzymatic re…
Poisson Hamiltonian Pontryagin Dynamics and Optimal Control of Mechanical Systems on Lie Groupoids
Ghorbanali Haghighatdoost
We develop a Poisson Hamiltonian formulation of Pontryagin dynamics for optimal control of mechanical systems on Lie groupoids. The reduced dynamics is formulated intrinsically on…
Geometric Dynamical Systems
Ghorbanali Haghighatdoost
This article provides a conceptual and historical review of the evolution of integrable Hamiltonian systems from the Moscow School of A. T. Fomenko to the emerging Azarbaijan Schoo…
Euler Poincare Dynamics and Control on Lie Groupoids
Ghorbanali Haghighatdoost
We extend the Euler Poincare formalism from Lie groups to Lie groupoids for optimal control problems. While Lie algebroids provide the standard infinitesimal framework, the groupoi…
Lie symmetry analysis and similarity reductions for the tempered-fractional Keller Segel system
Ghorbanali Haghighatdoost, Mustafa Bazghandi
We perform a Lie symmetry analysis on the tempered-fractional Keller Segel (TFKS) system, a chemo-taxis model incorporating anomalous diffusion. A novel approach is used to handle…
Optimal control problems on the co-adjoint Lie groupoids
Ghorbanali Haghighatdoost
In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie alg…
A note on integrabiliy of Hamiltonian systems on the co-adjoint Lie groupoids
Ghorbanali Haghighatdoost, Rezvaneh Ayoubi
As we said in our previous work [4], the main idea of our research is to introduce a class of Lie groupoids by means of co-adjoint representation of a Lie groupoid on its isotropy…
Right invariant Poisson Nijenhuis structures on Lie groupoids Correspondence and Classification
Ghorbanali Haghighatdoost
In this paper, we introduce right-invariant Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called (Poisson bivector, Nijenhuis operator) stru…