-
Previous Article
Anisotropically diffused and damped Navier-Stokes equations
- PROC Home
- This Issue
-
Next Article
A symmetric nearly preserving general linear method for Hamiltonian problems
Bifurcation without parameters in circuits with memristors: A DAE approach
1. | Depto. Matemática Aplicada a las Tecnologías de la Información, ETSI Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria s/n - 28040 Madrid, Spain, Spain |
References:
[1] |
B. Andrásfai, Introductory Graph Theory,, Akadémiai Kiadó, (1977). Google Scholar |
[2] |
B. Andrásfai, Graph Theory: Flows, Matrices,, Adam Hilger, (1991). Google Scholar |
[3] |
A. Ascoli, T. Schmidt, R. Tetzlaff and F. Corinto, Application of the Volterra series paradigm to memristive systems, in R. Tetzlaff (ed.),, Memristors and Memristive Systems, (2014), 163. Google Scholar |
[4] |
B. Bao, Z. Ma, J. Xu, Z. Liu and Q. Xu, A simple memristor chaotic circuit with complex dynamics,, Internat. J. Bifurcation and Chaos, 21 (2011), 2629. Google Scholar |
[5] |
D. Biolek, Z. Biolek and V. Biolkova, SPICE modeling of memristive, memcapacitive and meminductive systems,, Proc. Eur. Conf. Circuit Theor. Design 2009, (2009), 249. Google Scholar |
[6] |
B. Bollobás, Modern Graph Theory,, Springer-Verlag, (1998). Google Scholar |
[7] |
L. O. Chua, Memristor - The missing circuit element,, IEEE Trans. Circuit Theory, 18 (1971), 507. Google Scholar |
[8] |
L. O. Chua, C. A. Desoer and E. S. Kuh, Linear and Nonlinear Circuits,, McGraw-Hill, (1987). Google Scholar |
[9] |
F. Corinto, A. Ascoli and M. Gilli, Analysis of current-voltage characteristics for memristive elements in pattern recognition systems,, Internat. J. Circuit Theory Appl., 40 (2012), 1277. Google Scholar |
[10] |
M. Di Ventra, Y. V. Pershin and L. O. Chua, Circuit elements with memory: memristors, memcapacitors and meminductors,, Proc. IEEE, 97 (2009), 1717. Google Scholar |
[11] |
B. Fiedler, S. Liebscher, and J. C. Alexander, Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory,, J. Differential Equations, 167 (2000), 16. Google Scholar |
[12] |
B. Fiedler and S. Liebscher, Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws,, SIAM J. Math. Anal., 31 (2000), 1396. Google Scholar |
[13] |
B. Fiedler, S. Liebscher, and J. C. Alexander, Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary oscillations,, Internat. J. Bifur. Chaos, 10 (2000), 1613. Google Scholar |
[14] |
M. Itoh and L. O. Chua, Memristor oscillators,, Internat. J. Bifur. Chaos, 18 (2008), 3183. Google Scholar |
[15] |
M. Itoh and L. O. Chua, Memristor Hamiltonian circuits,, Internat. J. Bifur. Chaos, 21 (2011), 2395. Google Scholar |
[16] |
L. Jansen, M. Matthes and C. Tischendorf, Global unique solvability for memristive circuit DAEs of index 1,, Int. J. Circuit Theory Appl., (2014). Google Scholar |
[17] |
D. Jeltsema and A. Doria-Cerezo, Port-Hamiltonian formulation of systems with memory,, Proc. IEEE, 100 (2012), 1928. Google Scholar |
[18] |
O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi and D. Abbott, The fourth element: characteristics, modelling and electromagnetic theory of the memristor,, Proc. R. Soc. A, 466 (2010), 2175. Google Scholar |
[19] |
M. Messias, C. Nespoli and V. A. Botta, Hopf bifurcation from lines of equilibria without parameters in memristors oscillators,, Internat. J. Bifur. Chaos, 20 (2010), 437. Google Scholar |
[20] |
B. Muthuswamy and L. O. Chua, Simplest chaotic circuit,, Internat. J. Bifur. Chaos, 20 (2010), 1567. Google Scholar |
[21] |
Y. V. Pershin and M. Di Ventra, Neuromorphic, digital and quantum computation with memory circuit elements,, Proc. IEEE, 100 (2012), 2071. Google Scholar |
[22] |
Y. V. Pershin and M. Di Ventra, Memory effects in complex materials and nanoscale systems,, Advances in Physics, 60 (2011), 145. Google Scholar |
[23] |
R. Riaza, Differential-Algebraic Systems,, World Scientific, (2008). Google Scholar |
[24] |
R. Riaza, Nondegeneracy conditions for active memristive circuits,, IEEE Trans. Circuits and Systems - II, 57 (2010), 223. Google Scholar |
[25] |
R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits,, SIAM J. Appl. Math., 72 (2012), 877. Google Scholar |
[26] |
D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, The missing memristor found,, Nature, 453 (2008), 80. Google Scholar |
[27] |
C. Tischendorf, Coupled systems of differential algebraic and partial differential equations in circuit and device simulation. Modeling and numerical analysis,, Habilitationsschrift, (2003). Google Scholar |
show all references
References:
[1] |
B. Andrásfai, Introductory Graph Theory,, Akadémiai Kiadó, (1977). Google Scholar |
[2] |
B. Andrásfai, Graph Theory: Flows, Matrices,, Adam Hilger, (1991). Google Scholar |
[3] |
A. Ascoli, T. Schmidt, R. Tetzlaff and F. Corinto, Application of the Volterra series paradigm to memristive systems, in R. Tetzlaff (ed.),, Memristors and Memristive Systems, (2014), 163. Google Scholar |
[4] |
B. Bao, Z. Ma, J. Xu, Z. Liu and Q. Xu, A simple memristor chaotic circuit with complex dynamics,, Internat. J. Bifurcation and Chaos, 21 (2011), 2629. Google Scholar |
[5] |
D. Biolek, Z. Biolek and V. Biolkova, SPICE modeling of memristive, memcapacitive and meminductive systems,, Proc. Eur. Conf. Circuit Theor. Design 2009, (2009), 249. Google Scholar |
[6] |
B. Bollobás, Modern Graph Theory,, Springer-Verlag, (1998). Google Scholar |
[7] |
L. O. Chua, Memristor - The missing circuit element,, IEEE Trans. Circuit Theory, 18 (1971), 507. Google Scholar |
[8] |
L. O. Chua, C. A. Desoer and E. S. Kuh, Linear and Nonlinear Circuits,, McGraw-Hill, (1987). Google Scholar |
[9] |
F. Corinto, A. Ascoli and M. Gilli, Analysis of current-voltage characteristics for memristive elements in pattern recognition systems,, Internat. J. Circuit Theory Appl., 40 (2012), 1277. Google Scholar |
[10] |
M. Di Ventra, Y. V. Pershin and L. O. Chua, Circuit elements with memory: memristors, memcapacitors and meminductors,, Proc. IEEE, 97 (2009), 1717. Google Scholar |
[11] |
B. Fiedler, S. Liebscher, and J. C. Alexander, Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory,, J. Differential Equations, 167 (2000), 16. Google Scholar |
[12] |
B. Fiedler and S. Liebscher, Generic Hopf bifurcation from lines of equilibria without parameters: II. Systems of viscous hyperbolic balance laws,, SIAM J. Math. Anal., 31 (2000), 1396. Google Scholar |
[13] |
B. Fiedler, S. Liebscher, and J. C. Alexander, Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary oscillations,, Internat. J. Bifur. Chaos, 10 (2000), 1613. Google Scholar |
[14] |
M. Itoh and L. O. Chua, Memristor oscillators,, Internat. J. Bifur. Chaos, 18 (2008), 3183. Google Scholar |
[15] |
M. Itoh and L. O. Chua, Memristor Hamiltonian circuits,, Internat. J. Bifur. Chaos, 21 (2011), 2395. Google Scholar |
[16] |
L. Jansen, M. Matthes and C. Tischendorf, Global unique solvability for memristive circuit DAEs of index 1,, Int. J. Circuit Theory Appl., (2014). Google Scholar |
[17] |
D. Jeltsema and A. Doria-Cerezo, Port-Hamiltonian formulation of systems with memory,, Proc. IEEE, 100 (2012), 1928. Google Scholar |
[18] |
O. Kavehei, A. Iqbal, Y. S. Kim, K. Eshraghian, S. F. Al-Sarawi and D. Abbott, The fourth element: characteristics, modelling and electromagnetic theory of the memristor,, Proc. R. Soc. A, 466 (2010), 2175. Google Scholar |
[19] |
M. Messias, C. Nespoli and V. A. Botta, Hopf bifurcation from lines of equilibria without parameters in memristors oscillators,, Internat. J. Bifur. Chaos, 20 (2010), 437. Google Scholar |
[20] |
B. Muthuswamy and L. O. Chua, Simplest chaotic circuit,, Internat. J. Bifur. Chaos, 20 (2010), 1567. Google Scholar |
[21] |
Y. V. Pershin and M. Di Ventra, Neuromorphic, digital and quantum computation with memory circuit elements,, Proc. IEEE, 100 (2012), 2071. Google Scholar |
[22] |
Y. V. Pershin and M. Di Ventra, Memory effects in complex materials and nanoscale systems,, Advances in Physics, 60 (2011), 145. Google Scholar |
[23] |
R. Riaza, Differential-Algebraic Systems,, World Scientific, (2008). Google Scholar |
[24] |
R. Riaza, Nondegeneracy conditions for active memristive circuits,, IEEE Trans. Circuits and Systems - II, 57 (2010), 223. Google Scholar |
[25] |
R. Riaza, Manifolds of equilibria and bifurcations without parameters in memristive circuits,, SIAM J. Appl. Math., 72 (2012), 877. Google Scholar |
[26] |
D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, The missing memristor found,, Nature, 453 (2008), 80. Google Scholar |
[27] |
C. Tischendorf, Coupled systems of differential algebraic and partial differential equations in circuit and device simulation. Modeling and numerical analysis,, Habilitationsschrift, (2003). Google Scholar |
[1] |
Kie Van Ivanky Saputra, Lennaert van Veen, Gilles Reinout Willem Quispel. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 233-250. doi: 10.3934/dcdsb.2010.14.233 |
[2] |
Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete & Continuous Dynamical Systems - A, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209 |
[3] |
Jean Ginibre, Giorgio Velo. Modified wave operators without loss of regularity for some long range Hartree equations. II. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1357-1376. doi: 10.3934/cpaa.2015.14.1357 |
[4] |
Alexander Krasnosel'skii, Alexei Pokrovskii. On subharmonics bifurcation in equations with homogeneous nonlinearities. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 747-762. doi: 10.3934/dcds.2001.7.747 |
[5] |
Michael E. Filippakis, Donal O'Regan, Nikolaos S. Papageorgiou. Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1507-1527. doi: 10.3934/cpaa.2010.9.1507 |
[6] |
Jeremy L. Marzuola, Michael I. Weinstein. Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/Gross-Pitaevskii equations. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1505-1554. doi: 10.3934/dcds.2010.28.1505 |
[7] |
Mudassar Imran, Youssef Raffoul, Muhammad Usman, Chi Zhang. A study of bifurcation parameters in travelling wave solutions of a damped forced Korteweg de Vries-Kuramoto Sivashinsky type equation. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 691-705. doi: 10.3934/dcdss.2018043 |
[8] |
R. Ouifki, M. L. Hbid, O. Arino. Attractiveness and Hopf bifurcation for retarded differential equations. Communications on Pure & Applied Analysis, 2003, 2 (2) : 147-158. doi: 10.3934/cpaa.2003.2.147 |
[9] |
Tetsutaro Shibata. Global behavior of bifurcation curves for the nonlinear eigenvalue problems with periodic nonlinear terms. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2139-2147. doi: 10.3934/cpaa.2018102 |
[10] |
Patrick M. Fitzpatrick, Jacobo Pejsachowicz. Branching and bifurcation. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 1955-1975. doi: 10.3934/dcdss.2019127 |
[11] |
Sergiy Zhuk. Inverse problems for linear ill-posed differential-algebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 1467-1476. doi: 10.3934/proc.2011.2011.1467 |
[12] |
Ling-Hao Zhang, Wei Wang. Direct approach to detect the heteroclinic bifurcation of the planar nonlinear system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 591-604. doi: 10.3934/dcds.2017024 |
[13] |
Carlos Garca-Azpeitia, Jorge Ize. Bifurcation of periodic solutions from a ring configuration of discrete nonlinear oscillators. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 975-983. doi: 10.3934/dcdss.2013.6.975 |
[14] |
Rushun Tian, Zhi-Qiang Wang. Bifurcation results on positive solutions of an indefinite nonlinear elliptic system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 335-344. doi: 10.3934/dcds.2013.33.335 |
[15] |
Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu. Bifurcation of positive solutions for nonlinear nonhomogeneous Robin and Neumann problems with competing nonlinearities. Discrete & Continuous Dynamical Systems - A, 2015, 35 (10) : 5003-5036. doi: 10.3934/dcds.2015.35.5003 |
[16] |
Carmen Núñez, Rafael Obaya. A non-autonomous bifurcation theory for deterministic scalar differential equations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 701-730. doi: 10.3934/dcdsb.2008.9.701 |
[17] |
Kousuke Kuto, Tohru Tsujikawa. Bifurcation structure of steady-states for bistable equations with nonlocal constraint. Conference Publications, 2013, 2013 (special) : 467-476. doi: 10.3934/proc.2013.2013.467 |
[18] |
Shigui Ruan, Junjie Wei, Jianhong Wu. Bifurcation from a homoclinic orbit in partial functional differential equations. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1293-1322. doi: 10.3934/dcds.2003.9.1293 |
[19] |
S.M. Booker, P.D. Smith, P. Brennan, R. Bullock. In-band disruption of a nonlinear circuit using optimal forcing functions. Discrete & Continuous Dynamical Systems - B, 2002, 2 (2) : 221-242. doi: 10.3934/dcdsb.2002.2.221 |
[20] |
Gian-Italo Bischi, Laura Gardini, Fabio Tramontana. Bifurcation curves in discontinuous maps. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 249-267. doi: 10.3934/dcdsb.2010.13.249 |
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]