Related papers: The Inverse Variational Problem and Logistic Self-…
The logistic equation has been extensively used to model biological phenomena across a variety of disciplines and has provided valuable insight into how our universe operates. Incorporating time-dependent parameters into the logistic…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
Selfdual variational principles are introduced in order to construct solutions for Hamiltonian and other dynamical systems which satisfy a variety of linear and nonlinear boundary conditions including many of the standard ones. These…
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
The density of states of self-gravitational system diverges when the particles are spread to infinity. Other problem based an inhomogeneous distribution of particles,which motivate the gravitational interaction. In this sense the…
The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of…
We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law.…
A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
The Helmholtz conditions are necessary and sufficient conditions for a system of second order differential equations to be variational, that is, equivalent to a system of Euler-Lagrange equations for a regular Lagrangian. On the other hand,…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a…
The purpose of this paper is describe Lagrangian Mechanics for constrained systems on Lie algebroids, a natural framework which covers a wide range of situations (systems on Lie groups, quotients by the action of a Lie group, standard…
A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…
Self-regulation of living tissue as an example of self-organization phenomena in hierarchical systems of biological, ecological, and social nature is under consideration. The characteristic feature of these systems is the absence of any…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…