One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite...One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.展开更多
We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portrai...We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.展开更多
This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neuro...This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neurons in the hippocampal CA3 region and examine how strong coupling parameters modulate memory consolidation processes.Employing bifurcation analysis,we systematically characterize the model's complex dynamical behaviors.Subsequently,a characteristic waveform recognition algorithm enables precise feature extraction and automated detection of hippocampal sharp-wave ripples(SWRs).Our results demonstrate that neuronal rhythms exhibit a propensity for abrupt transitions near bifurcation points,facilitating the emergence of SWRs.Critically,temporal rhythmic analysis reveals that the occurrence of a bifurcation is not always sufficient for SWR formation.By integrating one-parameter bifurcation analysis with extremum analysis,we demonstrate that large-amplitude membrane potential oscillations near bifurcation points are highly conducive to SWR generation.This research elucidates the mechanistic link between changes in neuronal self-connection parameters and the evolution of rhythmic characteristics,providing deeper insights into the role of dynamical behavior in memory consolidation.展开更多
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.
基金supported by the National Natural Science Foundations of China(12371171)and the Natural Science Foundation of Jiangsu Province(BK20221339).
文摘We study the limit cycle bifurcations perturbing a class of quartic linear-like Hamiltonian systems having an elementary center at the origin. First, using methods of the qualitative theory, all possible phase portraits of the unperturbed system are found. Then, using the first order Melnikov function, Hopf bifurcation problem of the perturbed system is investigated, and an upper bound for the function is obtained near the origin.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272002 and 12372061)the R&D Program of Beijing Municipal Education Commission(Grant No.KM202310009004)+1 种基金the North China University of Technology(Grant No.2023XN075-01)the Youth Research Special Project of the North China University of Technology(Grant No.2025NCUTYRSP051)。
文摘This study investigates the bifurcation dynamics underlying rhythmic transitions in a biophysical hippocampal–cortical neural network model.We specifically focus on the membrane potential dynamics of excitatory neurons in the hippocampal CA3 region and examine how strong coupling parameters modulate memory consolidation processes.Employing bifurcation analysis,we systematically characterize the model's complex dynamical behaviors.Subsequently,a characteristic waveform recognition algorithm enables precise feature extraction and automated detection of hippocampal sharp-wave ripples(SWRs).Our results demonstrate that neuronal rhythms exhibit a propensity for abrupt transitions near bifurcation points,facilitating the emergence of SWRs.Critically,temporal rhythmic analysis reveals that the occurrence of a bifurcation is not always sufficient for SWR formation.By integrating one-parameter bifurcation analysis with extremum analysis,we demonstrate that large-amplitude membrane potential oscillations near bifurcation points are highly conducive to SWR generation.This research elucidates the mechanistic link between changes in neuronal self-connection parameters and the evolution of rhythmic characteristics,providing deeper insights into the role of dynamical behavior in memory consolidation.
