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[CT023]

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Chemical reactions link metabolites and form complex networks in living cells. We have previously developed “structural bifurcation analysis,” by which bifurcation properties of reaction systems are determined solely from network topologies. In this work, we establish a precise formalization connecting our analysis to conventional methods based on Jacobian matrices. The formalization increases applicability of the analysis, e.g. determining multistationarity, without assuming the full-rankedness of stoichiometric matrices or eliminations of equations/chemicals.
Classification : 34Hxx, 92Bxx, 34D10
Author(s) :
- Yong-Jin Huang (Division of Biological Sciences, Graduate School of Science, Kyoto University)
- Takashi Okada (Division of Biological Sciences, Graduate School of Science, Kyoto University)
- Atsushi Mochizuki (Institute for Life and Medical Sciences, Kyoto University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : The framework of port-Hamiltonian (pH) systems is a broadly applicable modeling paradigm. In this talk, we extend the scope of pH systems to time-delay systems. Our definition of a delay pH system is motivated by investigating the Kalman-Yakubovich-Popov inequality on the corresponding infinite-dimensional operator equation. Moreover, we show that delay pH systems are passive and closed under interconnection. We describe an explicit way to construct a Lyapunov-Krasovskii functional and discuss implications for delayed feedback.
Classification : 34K06, 37J06, 93C05, 34A09
Author(s) :
- Dorothea Hinsen (TU Berlin)
- Tobias Breiten (TU Berlin)
- Benjamin Unger (University of Stuttgart)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : {\bf Abstract.} In this talk, we discuss a newly introduced two step fixed point iterative algorithm. We prove a strong convergence result for weak contractions. We also prove stability and data dependency of a proposed iterative algorithm. Furthermore, we utilize our main result to approximate the solution of a nonlinear functional Volterra integral equation. Some numerical examples are also furnished. If time permits, then we will discuss Image recovery problem as well.
Classification : 34K07, 34K20, 47H08, 47H10, 41A25
Author(s) :
- Javid Ali (Aligarh Muslim University, Aligarh)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : We propose here a delay differential equation with a linear time coefficient that produces transient resonant behavior. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. Also, for an appropriately tuned value of the delay, the height of the power spectrum goes through the maximum. This resonant behavior contrasts itself against the general behaviors observed with the constant coefficient delay differential equations.
Classification : 34K23, 93C43
Author(s) :
- Kenta Ohira (Nagoya University)
- Toru Ohira (Graduate School of Mathematics, Nagoya University)

Session Date & Time : 5D (Aug.25, 15:30-17:10)
Type : Contributed Talk
Abstract : Delay differential equations are an interesting class of non-local equations that involve a function and its derivatives evaluated at different points in time. By introducing a new class of functions, we have been able to provide fundamental solutions for autonomous linear delay differential equations. These functions, referred to as delay functions, relate the power series solutions of ordinary differential and delay differential equations and can be easily extended to more generalised series solutions.
Classification : 34Kxx, 34K06, 44A10
Author(s) :
- Stuart-James Malouf Burney (University of New South Wales)
- Christopher Angstmann (University of New South Wales)
- Bruce Henry (University of New South Wales)
- Byron Jacobs (University of Johannesburg)
- Zhuang Xu (University of New South Wales)