Abstract
For certain parameters, the mapping of a Hassell-type recruitment population model has a chaotic attractor. The control parameter is disturbed slightly with time by the improvement OGY method. When the mapping point wanders to the neighborhood of the periodic point, the control parameter is perturbed. The chaotic motion is controlled on the stable periodic period-1 point and period-2 orbits, and the influence of different control parameter ranges on the control average time is analyzed. When the selected regulator poles are different, the number of iterations used to control chaotic motion on a stable periodic orbit is different. Numerical simulations are presented to illustrate our results with the theoretical analysis and show the effect of the control method.
Highlights
Leslie models [1] with nonlinear fertility and mortality can have complicated dynamical behavior
Where x and y stand for the density of the first age group and the second age group. a and ca are the group’s initial fertility rates (a, c > 0), b is the survival rate from the first age group to the second one, and λ is the decay index, λ > 0
In equation (1), the fertility rate monotonically decreases as a function of the total population size, and the fertility decay is exponential. e other model is Hassell model
Summary
Leslie models [1] with nonlinear fertility and mortality can have complicated dynamical behavior. E basic idea of controlling chaos can be understood by considering the following one-dimensional logistic map, one of the best studied chaotic systems: xn+1 f xn, r rxn 1 − xn,. Equation (5) holds only when the trajectory xn enters a small neighborhood of the period-m orbit, i.e., when |xn − x(i)| ≪ 1, and the required parameter perturbation Δrn is small. When the trajectory is outside the neighborhood of the target periodic orbit, any parameter perturbation is not applied, so the system evolves at its nominal parameter value r0. E chaos of high periodic states and high-dimensional dynamic systems in chaotic attractors is controlled by the improved OGY method. By the OGY method, Guo et al [11, 12] studied the chaos control of two-dimensional Lauwerier mapping
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