Some Combinatorial Aspects of Discrete Non-linear Population Dynamics
نویسندگان
چکیده
Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with immigration, and we also apply it to the famous logistic map. We also are able to give a number of results for the invariant density of this map, some being related to the Carleman linearization.
منابع مشابه
Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays
Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...
متن کاملOptimal discrete-time control of robot manipulators in repetitive tasks
Optimal discrete-time control of linear systems has been presented already. There are some difficulties to design an optimal discrete-time control of robot manipulator since the robot manipulator is highly nonlinear and uncertain. This paper presents a novel robust optimal discrete-time control of electrically driven robot manipulators for performing repetitive tasks. The robot performs repetit...
متن کاملSome combinatorial aspects of finite Hamiltonian groups
In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...
متن کاملEnhancement of Articulated Heavy Vehicle Stability by Optimal Linear Quadratic Regulator (LQR) Controller of Roll-yaw Dynamics
Non-linear characteristic of tire forces is the main cause of vehicle lateral dynamics instability, while direct yaw moment control is an effective method to recover the vehicle stability. In this paper, an optimal linear quadratic regulator (LQR) controller for roll-yaw dynamics to articulated heavy vehicles is developed. For this purpose, the equations of motion obtained by the MATLAB sof...
متن کاملUndirected Multiflow Problems and Related Topics - Some Recent Developments and Results
A multiflow (multicommodity flow), arising as a natural extension of the well-known notion of a network flow, is a popular object studied in linear programming and combinatorial optimization. We discuss some recent results on undirected multiflow problems and ideas behind them, concerning combinatorial and computational aspects, such as: (i) the existence of feasible and optimal solutions with ...
متن کامل