Local bifurcations and feasibility regions in differential-algebraic systems

Venkatasubramanian, V.; Schättler, Heinz; Zaborszky, J.

doi:10.1109/9.478226

Cited by 245 publications

(170 citation statements)

References 29 publications

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“…It follows from Theorem 3 in [20], when v increase through 0, one eigenvalue of system (24) moves from C − to C + along real axis by diverging through ∞. Hence, system (24) is unstable around P * andP * in the case of zero and positive economic interest, respectively.…”

Section: Qualitative Analysis Of Systemmentioning

confidence: 92%

“…It follows from simple computations that (27) Based on the above analysis, it can be concluded that existence theorem of singularity induced bifurcation (Theorem 3 in [20]) holds, hence system (24) has a singularity induced bifurcation around P * and the bifurcation value is v = 0.…”

Section: Qualitative Analysis Of Systemmentioning

confidence: 99%

“…The singularity induced bifurcation does not occur in usual ordinary differential equation system, which has been characterized for differential-algebraic system. More introductions of singularity induced bifurcation can be found in [20]. In order to eliminate singularity induced bifurcation.…”

Section: Qualitative Analysis Of Systemmentioning

confidence: 99%

See 2 more Smart Citations

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Liu¹,

Lü²,

Zhang³

et al. 2016

Applied Mathematics and Computation

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Section: Qualitative Analysis Of Systemmentioning

confidence: 92%

Section: Qualitative Analysis Of Systemmentioning

confidence: 99%

See 1 more Smart Citation

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Liu¹,

Lü²,

Zhang³

et al. 2016

Applied Mathematics and Computation

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“…At the bifurcation value G = 0 the matrix pencil displays one additional infinite eigenvalue (cf. the Appendix): this divergence through oo is reminiscent of a singularity-induced bifurcation [31,32], which in this case coexists with a (say, regular) zero-eigenvalue transition.…”

Section: Dynamical Features Of a Family Of R-mc-ml Circuitsmentioning

confidence: 99%

Second order mem‐circuits

Riaza

2014

Circuit Theory & Apps

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This paper presents a comprehensive taxonomy of so-called second order memory devices, which include charge-controlled memcapacitors and flux-controlled meminductors, among other novel circuit elements. These devices, which are classified according to their differential and state orders, are necessary to get a complete extension of the family of classical nonlinear circuit elements (resistors, capacitors, inductors) for all possible controlling variables. Using a fully nonlinear formalism, we obtain nondegeneracy conditions for a broad class of second order mem-circuits. This class of circuits is expected to yield a rich dynamic behavior; in this regard we explore certain bifurcation phenomena exhibited by a family of circuits including a charge-controlled memcapacitor and a flux-controlled meminductor, providing some directions for future research.

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“…Based on Theorem 3 in [19], system (1) has a singularity-induced bifurcation at the positive equilibrium point P * when bifurcation parameter m = 0. If m increases through zero, one eigenvalue of system (1) will move from C -(the open complex left half plane) to C + (the open complex right half plane) along the real axis by diverging into ∞, and thus the stability of the positive equilibrium point P * changes from stable to unstable.…”

Section: = E(t)(py(t) -C)mentioning

confidence: 99%

Variable structure control for a singular biological economic model with time delay and stage structure

Zhang

Wei

2017

Adv Differ Equ

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A singular biological economic model which considers a prey-predator system with time delay and stage structure is proposed in this paper. The local stability at the equilibrium point and the dynamic behavior of the model are studied. Local stability analysis of the model without time delay reveals that there is a phenomenon of singularity-induced bifurcation due to the economic equilibrium. Furthermore, the phenomenon of Hopf bifurcation of the model at the boundary equilibrium point occurs as the time delay satisfies certain conditions. In order to apply variable structure control to eliminate the complex behaviors caused by singularity-induced bifurcation, the singular model is transformed into a single-input and single-output model with parameter varying within definite intervals. Then variable structure control with sliding mode based on a power reaching law is designed to stabilize the model. Numerical simulations are given to verify the effectiveness of the conclusions.

show abstract

Local bifurcations and feasibility regions in differential-algebraic systems

Cited by 245 publications

References 29 publications

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Modeling and analysis in a prey–predator system with commercial harvesting and double time delays

Second order mem‐circuits

Variable structure control for a singular biological economic model with time delay and stage structure

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