The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of t...The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.展开更多
More and more biological evidences have been found that neural networks in the spinal cord, referred to as ＂central pattern generators＂ （CPGs）, govern locomotion. CPGs are capable of producing rhythmic movements, ...More and more biological evidences have been found that neural networks in the spinal cord, referred to as ＂central pattern generators＂ （CPGs）, govern locomotion. CPGs are capable of producing rhythmic movements, such as swimming, flying, and walking, even when isolated from the brain and sensory inputs. If we could build up any models that have similar functions as CPGs, it will be much easier to design better locomotion for robots. In this paper, a self-training environment is designed and through genetic algorithm （GA）, walking trajectories for every foot of AIBO are generated at first. With this acquired walking pattern, AIBO gets its fastest locomotion speed. Then, this walking pattern is taken as a reference to build CPGs with Hopf oscillators. By changing corresponding parameters, the frequencies and the amplitudes of CPGs＇ outputs can be adjusted online. The limit cycle behavior of Hopf oscillators ensures the online adjustment and the walking stability against perturbation as well. This property suggests a strong adaptive capacity to real environments for robots. At last, simulations are carried on in Webots and verify the proposed method.展开更多
In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation...In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10975043 and 10947166)the Natural Science Foundation of Hebei Province,China (Grant Nos. A2011201006 and A2010000185)the Science Foundation of Hebei University
文摘The controllable transition between Turing and antispiral patterns is studied by using a time-delayed-feedback strategy in a FitzHugh-Nagumo model. We treat the time delay as a perturbation and analyse the effect of the time delay on the Turing and Hopf instabilities near the Turing Hopf codimension-two phase space. Numerical simulations show that the transition between the Turing patterns （hexagon, stripe, and honeycomb）, the dual-mode antispiral, and the antispiral by applying appropriate feedback parameters. The dual-mode antispiral pattern originates from the competition between the Turing and Hopf instabilities. Our results have shown the flexibility of the time delay on controlling the pattern formations near the Turing-Hopf codimension-two phase space.
基金supported by National Natural Science Foundation of China (Grant No. 60875057)National Hi-tech Research and Development Program of China(863 Program, Grant No. 2009AA04Z213)
文摘More and more biological evidences have been found that neural networks in the spinal cord, referred to as ＂central pattern generators＂ （CPGs）, govern locomotion. CPGs are capable of producing rhythmic movements, such as swimming, flying, and walking, even when isolated from the brain and sensory inputs. If we could build up any models that have similar functions as CPGs, it will be much easier to design better locomotion for robots. In this paper, a self-training environment is designed and through genetic algorithm （GA）, walking trajectories for every foot of AIBO are generated at first. With this acquired walking pattern, AIBO gets its fastest locomotion speed. Then, this walking pattern is taken as a reference to build CPGs with Hopf oscillators. By changing corresponding parameters, the frequencies and the amplitudes of CPGs＇ outputs can be adjusted online. The limit cycle behavior of Hopf oscillators ensures the online adjustment and the walking stability against perturbation as well. This property suggests a strong adaptive capacity to real environments for robots. At last, simulations are carried on in Webots and verify the proposed method.
文摘In this paper, a spatial tri-trophic food chain model with ratio-dependent Michaelis-Menten type functional response under homogeneous Neumann boundary conditions is studied. Conditions for Hopf and Turing bifurcation are derived. Sufficient conditions for the emergence of spatial patterns are obtained. The results of numerical simulations reveal the formation of labyrinth patterns and the coexistence of spotted and stripe-like patterns.
