this paper investigates the dynamics and stability properties of a discrete-time lotka-volterra type system. we first analyze stability of the fixed points and the existence of local bifurcations. our analysis shows the presence of rich variety of local bifurcations, namely, stable fixed points; in which population numbers remain constant, periodic cycles; in which population numbers oscillate amo...

from the early 1950s, estimating the autocorrelations of polynomials with coefficients on the unit circle has found applications in ising spin systems and in surface acoustic wave designs. in this paper, a technique is introduced that not only estimates the autocorrelations, but for some special types of such polynomials, it locates the frequencies at which maximum autocorrelation occurs.

This paper describes a previously undocumented phenomenon in dynamical systems theory; namely, the occurrence of heteroclinic cycles that are structurally stable within the space of C vector fields equivariant with respect to a symmetry group. In the space X(M) of C vector fields on a manifold M, there is a residual set of vector fields having no trajectories joining saddle points with stable m...

Physical limits place bounds on the divergent behaviour of dynamical systems. The paper explores this situation, providing an example where generator field-voltage limits capture behaviour, giving rise to a stable, though non-smooth, limit cycle. It is shown that shooting methods can be adapted to solve for such non-smooth switching-induced limit cycles. By continuing branches of switching-indu...

The presence of the power-law memory is a significant feature many natural (biological, physical, etc.) and social systems. Continuous discrete fractional calculus instrument to describe behavior systems with memory. Existence chaotic solutions an intrinsic property nonlinear dynamics (regular fractional). Behavior can be very different from corresponding no Finding periodic points essential fo...