Simplified models of limit-cycle walking on flat terrain have provided important insights into the nature of legged locomotion. Real walking robots (and humans), however, do not exhibit true limit cycle dynamics because terrain, even in a carefully designed laboratory setting, is inevitably non-flat. Walking systems on stochastically rough terrain may not satisfy strict conditions for limit-cyc...

3 Stability 17 3.1 General definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Stability of linear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Linearization and stability of nonlinear systems . . . . . . . . . . . . . . . . . . 20 3.4 Lyapunov functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.5 Li...

In this paper, we suggest Gompertz Autoregressive model by using the cumulative distribution function of and, aim paper is studying and finding stability conditions a limit cycle for with period, giving some examples AR (1) to explain orbital stable or unstable plots trajectories different initial values.