Dynamical systems with large number of attractors and their dependence on the parameters?

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It is much important to study the attractors in a dynamical system as these indicate how the system behaves once the initial transients are discarded.



Also, the study of systems with many numbers of attractors are interesting as the parameters are varied.




I am looking for such examples of systems where there are many attractors in the dynamical systems and their dependence on the parameters.





soft-question dynamical-systems intuition visualization motivation




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  • If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
    – guluzhu
    Aug 22 at 6:54










  • Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
    – LutzL
    Aug 22 at 7:36














up vote
0
down vote

favorite












It is much important to study the attractors in a dynamical system as these indicate how the system behaves once the initial transients are discarded.



Also, the study of systems with many numbers of attractors are interesting as the parameters are varied.




I am looking for such examples of systems where there are many attractors in the dynamical systems and their dependence on the parameters.





soft-question dynamical-systems intuition visualization motivation




share|cite|improve this question






















  • If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
    – guluzhu
    Aug 22 at 6:54










  • Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
    – LutzL
    Aug 22 at 7:36












up vote
0
down vote

favorite









up vote
0
down vote

favorite











It is much important to study the attractors in a dynamical system as these indicate how the system behaves once the initial transients are discarded.



Also, the study of systems with many numbers of attractors are interesting as the parameters are varied.




I am looking for such examples of systems where there are many attractors in the dynamical systems and their dependence on the parameters.





soft-question dynamical-systems intuition visualization motivation




share|cite|improve this question














It is much important to study the attractors in a dynamical system as these indicate how the system behaves once the initial transients are discarded.



Also, the study of systems with many numbers of attractors are interesting as the parameters are varied.




I am looking for such examples of systems where there are many attractors in the dynamical systems and their dependence on the parameters.






soft-question dynamical-systems intuition visualization motivation





share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 22 at 7:03









iadvd

5,37992555




5,37992555










asked Aug 22 at 6:26









BAYMAX

2,55021021




2,55021021











  • If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
    – guluzhu
    Aug 22 at 6:54










  • Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
    – LutzL
    Aug 22 at 7:36
















  • If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
    – guluzhu
    Aug 22 at 6:54










  • Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
    – LutzL
    Aug 22 at 7:36















If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
– guluzhu
Aug 22 at 6:54




If the attractor means the equilibrium point of the system. Then, consider the system: $dotx_1=omega x_2$, $dotx_2=-omega x_1$. The system is marginally stable, whose solution is periodic and a circle on the 2D plane. The radius of the circle is given by $sqrtx_1(0)^2+x_2(0)^2$. The number of the attractors is infinite because it is a set.
– guluzhu
Aug 22 at 6:54












Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
– LutzL
Aug 22 at 7:36




Could the "Ueda-Duffing equation with forcing" like in this question be an example for your question?
– LutzL
Aug 22 at 7:36















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