It is shown that all simple ecological, i.e. population dynamical equations (unlimited exponential population growth (or decrease) dynamics, logistic or Verhulst equation, usual and generalized Lotka-Volterra equations) hold a symmetry, called CEPT symmetry. Namely, all simple ecological dynamical equations are invariant (symmetric) in respect to successive application of the time reversal tran...

We consider discrete invertible dynamical systems L with the property that the kth iterate L k possesses (reversing) symmetries that are not possessed by L. A map U is called a (reversing) k-symmetry of L if k is the smallest positive integer for which U is a (reversing) symmetry of L k. In this paper we discuss the particular case that L possesses a cyclic reversing k-symmetry group. We derive...

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program constructs and investigates phase portraits of discrete dynamical systems modulo groups of their symmetries, searches dynamical systems possessing specific properti...

We discuss some aspects of confinement and dynamical symmetry breaking in the so-called nonabelian Argyres-Douglas vacua, which occur very generally in supersymmetric theories. These systems are characterized by strongly-coupled nonabelian monopoles and dyons; confinement and dynamical symmetry breaking are caused by the condensation of monopole composites, rather than by condensation of single...

We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously broken at finite as well as zero temperatures, implying the existence of classical and quantum phase transitions with a nontrivial critical behavior. The dynami...