# Ravindra E Amritkar

**M.Sc.**: IIT Bombay (1973)

**Ph.D.**: IISc Banglore (1978)

**Post-Doctoral**: IISc Banglore (1979-81)

**Research Areas**: Nonlinear Phenomena and chaos, Complex systems, networks.

# Awards

- Meghnad Saha award for theoretical sciences (1995)

# Research Work

#### Significant Research Contributions

- Coupled map lattices

(i) The rst systematic analysis of the problem of the stability of spatially and temporally periodic solutions to coupled map lattice systems is done. It is shown that the problem can be reduced to the study of eigenvalues of matrices of much smaller

- Spatial synchronization and extinction

We show that a species rst undergoes spatial synchronization and then extinction. Thus a species cannot survive in isolated locations and cannot avoid extinction. The reason for this behavior is the competitive nature of interaction between members of

- Characterization of chaotic systems

(i) Mutual correlations : A novel method of characterizing correlations between dynamical variables is introduced by dening mutual correlation exponents. These exponents are geometric in nature and provide information about the system which is not eas

- Extreme events

We analyse extreme events on complex networks using the random walk model where the extreme events are dened as surpassing of the ux above a prescribed threshold. We nd that the nodes with smaller number of links are more prone to extreme events th

- Wavelength doubling bifurcations

This is the rst report of the observation of wavelength doubling bifurcations. The phenomena is observed in coupled map lattices. An analytic criterion for the observation of the phenomena is also obtained. The result is an important step in our under

- Control of chaos

(i) It is shown that a combination of adaptive control and synchronization can be used to estimate parameters of the system. (Phys. Rev. E 59, 284 (1999); Phys. Rev. E 61, 4986 (2000).) (ii) A novel idea of enhancing chaos in chaotic systems is suggest

- Complex Networks

(i) It is shown that coupled map dynamics on complex networks gives rise to phase synchronized clusters. Two interesting results are obtained. First, two types of clusters, self-organized and driven are identied. In self-organized clusters most of the

- Aggregation

The rst analytic calculation for the limiting fan density and the critical angle for ballistic aggregation is given. Interesting scaling properties for the densities are found numerically. The study of percolation on the aggregates has given useful in

- Amplitude death

An important phenomenon in coupled dynamical systems is amplitude death where the dynamics of the coupled systems is quenched or suppressed while the individual systems oscillate when uncoupled. We introduce a general mechanism for amplitude death in c

#### Invited Talks - Have given 62 invited and plenary talks in i

- Discussion meeting on Spatio-temporal physics

25 to 27 February 1999, RAC, Ooty. An invited talk on “Small World Network”.

- Workshop on Critical Phenomena and Complex Systems,

Aug. 14, 2012, Academia Sinica, Taipei, Invited talk on “Amplitude death in coupled dynamical systems”

- Conference on Computational Physics 2009,

16-19 Dec. 2009, Kaohsiung, Taiwan, Invited talk on “Estimating Parameters of a Dynamical System from the Time Series”.

- International workshop and conference on Statistical Physics Approach to Multidisciplinary problems,

IIT, Guwahati, Jan. 7-13, 2008, Two invited talks on “Networks and synchronization”

- Statphys-Kolkata IV, Complex networks: structure, function and processes, 22June-1July, 2004, S. N. Bose National Center for Basic Sciences, Kolkata.

An invited talk on “Coupled dynamics on complex networks”.

- Symposium on Complex systems : From Physics to Biology

Oct. 14-15, 2013, Jawaharlal Nehru University, New Delhi Invited talk on “Synchronization of coupled nearly identical dynamical systems”.

- Workshop on Nonlinear Waves and Turbulence

18 to 31 Dec. 1991, JNU, New Delhi. Two invited talks on (a) Multifractals (b) Coupled map lattices.

- Computational methods for nonlinear dynamics,

Sept. 22-25, 2010, Bharathidasan Univ., Tiruchirapalli, Talks on “Multifractal analysis and f − α spectrum” and “Estimating parameters of a dynamical system from a time series”.

- National Conf. on Nonlinear Sys. and Dynamics,

University of Madras, Chennai, February 6-8, 2006, An invited talk on “Control of chaos and synchronization”.

- Symposium on Statistical Physics

Feb. 1-3, 2014, Department of Physics, Indian Institute of Science, Bangalore Invited talk on “Synchronization of coupled nearly identical dynamical systems”.

- Academy discussion meeting on Theoretical approaches to molecular electronic structure and properties

16 to 18 Dec. 1994, Dept. of Chemistry, Uni. of Pune, Pune. A talk on “Enhancement of mixing in chaotic flows”

- National workshop on Nonlinear dynamical systems,

July, 4-8, 2011, NIT, Durgapur Two invited talks on “Synchronization of networks” and “Time delay systems”.

- International Conference on Nonlinear Dynamical Systems and Turbulence,

IISc, Bangalore, July 17-22, 2008, Invited talk on “Synchronization of time-varying networks”.

- International workshop on Biophysics and Complex systems,

10-15 Dec. 2009, Taipei, Taiwan, Invited talk on “Synchronization of Networks”.

- Conference and Research Workshop: Perspectives on Nonlinear Dynamics,

ICTP, Trieste, Italy, 16-27 July, 2007. (1) An invited talk on “Glassy state of coupled dynamical systems”. (2) A pedagogical lecture on “Synchronization”.

- International conference on Nonlinear dynamics: Integrability and chaos

12 to 16 Feb. 1998, Bharathidasan University, Thiruchirapalli. An invited talk on “Estimating parameters using synchronization and adaptive control”.

- Conference on Dynamics Days, Asia Pacific 7, Aug. 6 - 9, 2012, Academia Sinica, Taipei, Taiwan,

Invited talk “Extreme events on complex networks and network failure”.

- International Conference on Nonlinear Phenomena, 5-10 Jan., IISc, Bangalore (2004).

An invited talk on “Coupled dynamics in networks”.

- Conference on Perspectives in nonlinear dynamics,

July 15-18, 2013, University of Hyderabad Invited talk on “Extreme events on networks and network vulnerability”.

- Miniworkshop on Nonlinearity : Fractals, Pattern Formation, . . .

11 June to 6 July 1991, ICTP, Trieste, Italy. Three invited talks on (a) Geometric Correlations and multifractals, (b) Periodic orbits in coupled map lattices and (c) Generalized shift maps.

- AICTE-SDP staff developmemt program on Mathematical Applications in Engineering Profession,

June 21-July 02, 2010, L. J. Institute of Engineering and Technology, Ahmedabad, Talk on “Introduction to nonlinear dynamics and chaos”.

- SERC school on Nonlinear Dynamics II,

4-7 Jan. 2006, University of Podicherry, Pondicherry, 12 lectures on “Introduction to nonlinear dynamics”.

- National symposium on Nonequilibrium statistical physics & nonlinear dynamics,

Jan. 2-4, 2014, Indian Association for Cultivation of Science Invited talk on “Extreme events on complex networks”.

- Solid State Physics Symposium, DAE

27 to 31 Dec. 1993, BARC, Bombay. An invited talk on “Fractals and growth processes”

- 19th IEEE workshop on Nonlinear dynamics in electronic systems,

March 8-11, 2011, IICB and SINP, Kolkata, Invited talk on “Amplitude death in coupled dynamical systems”.

- SERC school on Nonlinear Dynamics IV,

June 26 - July 26, 2008, IISc Bangalore, 9 lectures on “Discrete dynamical systems and characterization of nonlinear systems” (June 30-July 4).

- Indo-Russian workshop on Complex Networks: Dynamics and Synchronization,

Dec. 1-2, 2009, IICB, Kolkata, Invited talk on “Synchronization of complex networks”.

- Meeting on Assembly, organization and propulsion in complex systems,

IIT, Chennai, 22-24 Feb. 2007, An invited talk on “Multicluster synchronization”.

- Golden Jubilee Conference on Nonlinear Dynamics & Computational Physics

18 to 22 November, 1997, PRL, Ahmedabad. An invited talk on “Estimating parameters using synchronization and adaptive control”.

- National Conf. on Nonlinear Sys. and Dynamics 7,

July 12-15, 2012, IISER, Pune Plenary talk on “Synchronization of coupled non identical dynamical systems”.

- Inter-disciplinary Workshop on: Probability and Statistical Physics

19 to 23 February 2001, S. N. Bose National Center for Basic Sciences, Calcutta. An invited talk on “Small World Network”.

- International Symposium on Extreme events: Modeling, Analysis, and Prediction,

Feb. 13 - 15, 2013, Hannover, Germany Plenary talk on “Extreme events on complex networks”.

- Seminar on Fractals

21 to 23 Feb. 1991, University of Hyderabad. An invited talk on “Applications of multifractals”

- DST meeting

April 2-3, 2010, Bharathidasan Univ., Tiruchirapalli, “Synchronization: time varying networks and variable delay”.

- 2005 NCTS Workshop on Critical Phenomena and Complex Systems, 11-12 March 2005, Department of Physics, National Taiwan University, Taipei.

An invited talk on “Synchronization in Coupled Dynamical Systems”.

- Conference on Chaos, solitons and fractals,

Nov. 29, 2013, Amsterdam, Netherlands Invited talk on “Extreme events on complex networks”.

- Workshop on Turbulence as a problem in physics

13 to 17 Dec. 1993, Jawaharlal Nehru Center, IISc, Bangalore. An invited talk on “Wavelength doubling bifurcations in spatio-temporal systems.”

- International Conference on Mathematical Biology,

July 04-07, 2011, IISC, Bangalore, Invited talk on “Amplitude death in coupled dynamical systems: Application to Alzxheimer’s disease”.

- Santa Fe Institute, Santa Fe, USA, March 10, 2008.

Seminar on “Synchronization of networks”.

- Third International Conference on Complex Systems and Applications,

June 29 - July 02, 2009, Le Havre, France, Invited talk on “Synchronization of time-varying networks”.

- SERC school on Nonlinear Dynamics III,

3-23 December 2006, IACS Kolkata, 6 lectures on “Synchronization”.

- March 14-15, 2014, Tezpur

Talk on “Synchronization”

- International conference on Dynamical systems

10 to 15 Jan. 1997. I.I.Sc. Bangalore. An invited talk on “Enhancing chaos in chaotic systems”.

- Conference on Statistical Physics and Nonlinear Dynamics,

March 12-16, 2012, S. N. Bose National Center for Basic Sciences, Kolkata, Invited talk on “Amplitude death in coupled dynamical systems”.

- Discussion Meeting on Nonequilibrium statistical mechanics

15 to 25 November 1999, IISc, Bangalore. An invited talk on “Small World Network”.

- Visit to University of Oldenburg,Oldenburg, Germany, Feb. 11-12, 2013

Seminar on “Amplitude death in coupled dynamical systems”.

- Workshop on Chaos

7 to 17 Feb. 1989, S. N. Bose Center, Calcutta. Two invited talks on “Unstable periodic orbits.”

- School on mathematical models,

14-25 June, 2010, L. J. Institute of E & T, Ahmedabad, Talk on “Introduction to nonlinear dynamics and chaos”

- International Conference on Recent developments in Nonlinear Dynamics,

Feb. 13-16, 2008, Bharathidasan Univ., Tiruchirapalli, Invited talk on “Glassy state of coupled dynamical systems”.

- The 2005 Annual Meeting of Physical Society of Republic of China, 1-3 Feb. 2005, National Sun Yat-Sen University, Kaoshiung, Taiwan.

An invited talk on “Synchronization of Coupled Dynamics on Complex Networks”.

- Visit to S. N. Bose Center, Kolkata, Nov. 1, 2013

Colloquium on “Extreme events on complex networks”.

- Workshop on Chaos : Some open problems

23 to 26 Aug. 1992, Jawaharlal Nehru Center, IISc, Bangalore. An invited talk on “Geometric correlations and multifractals”

- Conference on complex and biological systems,

July 2-3, 2011, St. Zavier College, Ahmadabad, Invited talk on “Neuronal networks with coupling through amyloid beta: towards a theory for Alzaeimers disease”.

- National Conf. on Nonlinear Sys. and Dynamics,

March 5-7, 2009, Saha Inst. Nuclear Phys., Kolkata, Plenary talk on “Estimating parameters of a dynamical system”.

- National conference on ”Mathematical Foundations of Coding, Complexity, Computation and Cryptography”

IISc, Bangalore, July 20-22, 2006, An invited talk on “Chaotic & Non Linear Dynamical Systems for Encryption”.

- 3rd International Symposium on Complex Dynamical Systems and Applications (CDSA -2014)

March 10 ? 12, 2014, Indian Statistical Institute, Kolkata Invited talk on “Synchronization of coupled nearly identical dynamical systems”.

- Meeting on Dynamics of complex systems

6 to 11 Aug. 1995, S.N. Bose Inst., Calcutta. An invited talk on “Patterns and structures in coupled map lattices”.

- 2nd International Symposium On Complex Dynamical Systems and Applications,

January 9-11, 2012, Presidency University, Kolkata, India. Invited talk on “Synchronization with variable delay”.

- Workshop on Nonlinear Dynamics 4 to 6 November 1999, University of Hyderabad, Hyderabad.

An invited talk on “Estimating initial conditions from a time series”.

- Visit to National Chengchi University, Wenshan District,Taipei City, Taiwan,

Oct. 15, 2012 Colloquium on “Extreme events on complex networks”.

- Conference on Evolution of Complex Systems,

Jan. 13-15, 2010, IISc, Bangalore, Invited talk on “Synchronization of networks”.

- Hands-on Research on Complex Systems – Winter school,

IPR, Ahmedabad, Jan. 6-18, 2008, Invited talk on “Synchronization of coupled dynamical systems”.

- Perspectives in nonlinear dynamics, 12-15 July, 2004, IITM, Chennai.

An invited talk on “Coupled nonlinear dynamics on complex networks”.

- Inspire program, Oct. 21-26, 2013, Science City, Ahmedabad

Popular talk on “Beauty of Fractals”.

- Short term course on Chaotic dynamics

16 to 28 March 1992, IUC, Indore. Five lecture course on “Methods of characterization of chaos.”

- Symposium on Dynamics on Networks

Feb. 18-19, 2011, IISER, Pune, Talk on “Synchronization of dynamical systems on networks”.

- SERC school on Nonlinear Dynamics V,

Feb. 2-21, 2009, Institute of Advanced Study in Science and Technology, Gawahati, 6 lectures on “Characterization of Chaotic Systems”.

- The 8th Taiwan International Symposium on Statistical Physics (StatPhysTaiwan-2006),

Academia Sinica, Taipei, Taiwan, June 21-26, 2006, An invited talk on “Spatially synchronous extinction of species under external forcing”

- SERC school on Nonlinear Dynamics XI,

Feb. 4-7, 2014, Physics Department, Panjab University, Chandigarh Four lectures on “Characterization of Chaos”.

- National Seminar on Computational aspects in chaos and nonlinear dynamics

21 to 25 March 1994, Maharaja College, Cochin. An invited talk on “Wavelength doubling bifurcations in spatio-temporal systems”

- SERC school on Nonlinear Dynamics VIII,

Dec., 4-24, 2011, IISER, Pune Eight lectures on “Introduction to nonlinear dynamics”.

#### Research Students

- Workshop on Critical Phenomena and Complex Systems

Sept. 1 - 2, 2012, National Formosa University, Huwei, Yunlin, Taiwan, Invited talk on “Synchronization of coupled non identical dynamical systems”

- Seven students have completed their Ph.D. under my guidance.

# Teaching And Educational Contributions

# Papers In Journals

- Inverse problem for multifractals : Extension to logarithmic and additive corrections,

R. E. Amritkar and N. Gupte, Phys. Rev. Lett. 60, 245–248 (1988).

- Synchronized state of coupled dynamics on time-varying networks,

R. E. Amritkar and C. K. Hu, Chaos 16, 015117–1-5 (2006).

- Percolation of finite-sized objects on a lattice,

R. E. Amritkar and M. Roy, Phys. Rev. E 57, 1269–1272 (1998).

- Wavelength doubling bifurcations in coupled map lattices

R. E. Amritkar and P. M. Gade, Phys. Rev. Lett. 70, 3408–3411 (1993).

- Extreme event-size fluctuations in biased random walks on networks,

V. Kishore, M. S. Santhanam, and R. E. Amritkar, Phys. Rev. E 85, 056120 (2012).

- Characterizing loss of memory in a dynamical system using multifractals,

P. M. Gade and R. E. Amritkar, Phys. Rev. Lett. 65, 389–392 (1990).

- Computing the multifractal spectrum from time series: An algorithmic approach,

K. P. Harikrishnan, R. Misra, G. Ambika, and R. E. Amritkar, Chaos 19, 043129–1-9 (2009).

- A triple well potential model for the structural transition in Cu2Mo6S8

R. E. Amritkar, Solid State Comm. 40, 785 (1981).

- Dynamic algorithm for parameter estimation and its applications,

A. Maybhate and R. E. Amritkar, Phys. Rev. E 61, 6461–6470 (2000).

- Coherent structures in coupled map lattices,

J. K. John and R. E. Amritkar, Phys. Rev. E 51, 5103–5105 (1995).

- Characterizing loss of memory in chaotic dynamical systems,

R. E. Amritkar and P. M. Gade, Int. J. Mod. Phys. B 5, 2323 – 2345 (1991).

- Extreme Events on Complex Networks,

V. Kishore, M. S. Santhanam and R. E. Amritkar, Phys. Rev. Lett. 106, 188701–1-4 (2011).

- Theory of growth of ballistic aggregates,

A. V. Limaye and R. E. Amritkar, Phys. Rev. A 34, 5085–5090 (1986).

- Self-organized and driven synchronization in coupled map networks,

S. Jalan and R. E. Amritkar, Physica A 321, 220–225 (2003).

- Effect of noise on coupled chaotic systems,

M. Roy and R. E. Amritkar, Pramana 48, 271–285 (1997).

- Synchronization of chaotic orbits: The influence of unstable periodic orbits,

N. Gupte and R. E. Amritkar, Phys. Rev. E 48, R1620–R1623 (1993).

- Amplitude death in complex networks induced by environment,

V. Resmi, G. Ambika, R. E. Amritkar and G. Rangarajan, Phys. Rev. E 85, 046211–1-7 (2012).

- Effect of fluctuations on Multifractals,

N. Gupte, A. D. Gangal and R. E. Amritkar, Phys. Rev. A 36, 4950–4956 (1987).

- Synchronized clusters in coupled map networks II. Stability analysis,

R. E Amritkar, S. Jalan and C. K. Hu, Phys. Rev. E 72, 016212–1-9 (2005).

- Exponential dimension : Thermodynamic formalism and inversion,

N. Gupte and R. E. Amritkar, Phys. Rev. A 41, 4285–4293 (1990).

- Estimating parameters of a nonlinear dynamical system,

R. E. Amritkar, Phys. Rev. E 80, 047202–1-4 (2009).

- Observability of conduction electron spin resonance (CESR) in superconductors,

R. E. Amritkar, N. Kumar and R. Srinivasan, Solid State Comm. 38, 1095 (1981).

- Stochastic hierarchical model for cluster-cluster aggregation,

R. E. Amritkar, Phys. Rev. E 60, 4986–4989 (1999).

- Fractals and growth processes,

R. E. Amritkar, Indian J. Pure Appl. Phys. 32, 595 – 601 (1994).

- Characterizing loss of memory in chaotic dynamical systems,

R. E. Amritkar and P. M. Gade, Int. J. Mod. Phys. B 5, 2323 – 2345 (1991).

- Desynchronization bifurcation of coupled nonlinear dynamical systems,

S. Acharyya and R. E. Amritkar, Chaos 21, 023113–1-6 (2011).

- Exchange and correlation potential for a two dimensional electron gas at finite temperatures,

S. Phatisena, R. E. Amritkar and P. V. Panat, Phys. Rev. A 34, 5070–5079 (1986).

- Self-organized and driven synchronization in coupled maps,

S. Jalan and R. E. Amritkar, Phys. Rev. Lett. 90, 014101–1-4 (2003).

- Observation of stochastic coherence in coupled map lattices,

M. Roy and R. E. Amritkar, Phys. Rev. E 55, 2422–2425 (1997).

- P. M. Gade and R. E. Amritkar, Phys. Rev. E 47, 143–154 (1993).

R. E. Amritkar and N. Gupte, Phys. Rev. E 47, 3889–3895 (1993).

- Experimental evidence of synchronization of time-varying dynamical network,

S. K. Bhowmick, R. E. Amritkar and S. K. Dana, Chaos 22, 023105–1-9 (2012).

- Scaling and shadowing effects in ballistic aggregation,

P. S. Joag, A. V Limaye and R. E. Amritkar, Phys. Rev. A 36, 3395–3398 (1987).

- Synchronized clusters in coupled map networks I. Numerical studies,

S. Jalan, R. E Amritkar and C. K. Hu, Phys. Rev. E 72, 016211–1-15 (2005).

- A nonsimultaneous hierarchy : multifractal analysis,

R. E. Amritkar and N. Gupte, Phys. Rev. A 41, 3081–3089 (1990).

- Anticipatory synchronization with variable time delay and reset,

G. Ambika and R. E. Amritkar, Phys. Rev. E 79, 056206–1-11 (2009).

- Coherence factors in an excitonic insulator,

R. E. Amritkar and N. Kumar, Solid State Comm. 26, 727 (1978).

- Characterization and control of small-world networks,

S. A. Pandit and R. E. Amritkar, Phys. Rev. E 60, R1119–R1122 (1999).

- Synchronization of unstable orbits using adaptive control,

J. K. John and R. E. Amritkar, Phys. Rev. E 49, 4843–4848 (1994).

- Experimental observation of extreme multistability in an electronic system of two coupled Rssler oscillators

M. S. Patel, U. Patel, A. Sen, G. C. Sethia, C. Hens, S. K. Dana, U. Feudel, K. Showalter, C. N. Ngonghala, and R. E. Amritkar Phys. Rev. E 89, 022918 (2014).

- Stability of periodic orbits of coupled map lattices,

R. E. Amritkar, P. M. Gade, A. D. Gangal and V. M. Nandakumaran Phys. Rev. A 44, R3407–R3410 (1991).

- Synchronized states in chaotic systems coupled indirectly through dynamic environment,

V. Resmi, G. Ambika and R. E. Amritkar, Phys. Rev. E 81, 046216–1-7 (2010).

- Specific heat of two dimensional electron gas in the exchange only approximation,

R. E. Amritkar and P. V. Panat, J. Phys. C 18, 837–845 (1985).

- Estimation of initial conditions and secure communication,

A. Maybhate, R. E. Amritkar and D. R. Kulkarni, Int. J. Bif. Chaos, 13, 3079–3084, (2003).

- Enhancing chaos in chaotic maps and flows,

N. M. Gupte and R. E. Amritkar, Phys. Rev. E 54, 4580–4585 (1996).

- Spatially periodic orbits in coupled map lattices,

P. M. Gade and R. E. Amritkar, Phys. Rev. E 47, 143–154 (1993).

- Delay or anticipatory synchronization in one-way coupled systems using variable delay with reset,

G. Ambika, G. and R. E. Amritkar, Pramana 77, 891-904 (2011).

- Dimensional characterization of sets with partial scaling symmetry

R. E. Amritkar, A. D. Gangal and N. Gupte, Phys. Rev. A 36, 2850–2861 (1987).

- Synchronization of coupled chaotic dynamics on networks,

R. E. Amritkar and S. Jalan, Pramana 64, 455-464 (2005).

- Percolation on ballistic aggregates,

A. V. Limaye and R. E. Amritkar, Phys. Rev. B 40, R881–R883 (1989).

- Synchronization of networks,

R. E. Amritkar, Pramana 71, 195-201 (2008).

- A semi phenomenological theory of superfluid liquid 3He

R. E. Amritkar and N. Kumar, Curr. Sci. 43, 366 (1974).

- Nature of transitions in augmented discrete nonlinear Schr¨odinger equations,

R. E. Amritkar and V. M. Kenkre, Phys. Rev. E 59, 6306–6311 (1999).

- Wavelength doubling bifurcations in one–dimensional coupled logistic maps,

P. M. Gade and R. E. Amritkar, Phys. Rev. E 49, 2617–2622 (1994).

- Generalized synchronization of coupled chaotic systems

S. Acharyya and R. E. Amritkar EPJ-ST 222, 939 (2013).

- Quantitative measure of correlations: Synchronization and asynchronization,

R. E. Amritkar and N. Gupte, Phys. Rev. A 44, R3403–R3406 (1991).

- Parametric characterisation of a chaotic attractor using the two scale Cantor measure,

K.P. Harikrishnan, R. Misra, G. Ambika, R.E. Amritkar, Physica D 239, 420-427 (2010).

- A simple model for the structural transition in Cu3Mo6S8

D. S. Gawale and R. E. Amritkar, Indian J. Pure Appl. Phys. 22, 82 (1984).

- Decoding of signal from phase modulated unstable periodic orbit,

D. K. Kulkarni and R. E. Amritkar, Int. J. Bif. Chaos, 11, 3133–3138 (2001).

- Structures in coupled map lattices

R. E. Amritkar, Physica A 224, 382–389 (1996).

- Multifractals and partially scaling sets,

R. E. Amritkar, Indian J. Phys. 66A, 429 – 455 (1992).

- Synchronizing time delay systems using variable delay in coupling,

G. Ambika and R. E. Amritkar, Chaos, Solitons and Fractals 44 1035-1042 (2011).

- The excitonic theory for high temperature superconductivity in YBa2Cu3O7.

Part II, A. P. B. Sinha, P. V. Panat and R. E. Amritkar, Phase Transitions 10, 213–218 (1987).

- Coupled dynamics on networks,

S. Jalan and R. E. Amritkar, Physica A 346, 13–19 (2005).

- New dimension in multifractals : The exponential dimension,

N. Gupte and R. E. Amritkar, Phys. Rev. A 39, 5466–5469 (1989).

- Spatially synchronous extinction of species under external forcing,

R. E. Amritkar and G. Rangarajan, Phys. Rev. Lett. 96, 258102–1-4 (2006).

- A semi phenomenological theory of the two phase transitions in liquid 3He below 3 mK

R. E. Amritkar and N. Kumar, Lett. Neuovo Cim. 10, 81 (1974)

- Use of synchronization and adaptive control in parameter estimation from a time series, 1

A. Maybhate and R. E. Amritkar, Phys. Rev. E 59, 284–293 (1999).

- Synchronization by feedback and adaptive control,

J. K. John and R. E. Amritkar, Int. J. Bifurcation Chaos 4, 1687–1695 (1994).

- Synchronization of coupled nonidentical dynamical systems,

S. Acharyya and R. E. Amritkar, EPL 99, 40005 (2012).

- Role of apex oxygen and redox elements in high temperature superconductors,

R. E. Amritkar, D. G. Kanhere, P. V. Panat and A. P. B. Sinha, Bull. Mater. Sci. 14, 1079–1081 (1991).

- Stability of multi-cluster synchronization,

R. E. Amritkar and G. Rangarajan, Int. J. Bif. Chaos 19, 4263–4271 (2009).

- Effect of screening on exchange effects of inhomogeneous electron gas at finite temperature,

P. V. Panat and R. E. Amritkar, Phys. Rev. A 28, 1859 (1983).

- Random spread on the family of small-world networks,

S. A. Pandit and R. E. Amritkar, Phys. Rev. E 63, 041104–1-7 (2001).

- Interpolation of missing data using nonlinear and chaotic system analysis,

R. E. Amritkar and Pradeep Kumar, J. Geophys. Res. D2, 100, 3149–3154 (1995).

- Loss of memory in a chaotic dynamical systems,

P. M. Gade and R. E. Amritkar, Phys. Rev. A 45, 725–733 (1992).

- General mechanism for amplitude death in coupled systems,

V. Resmi, G. Ambika and R. E. Amritkar, Phy. Rev. E 84, 046212–1-12 (2011).

- An excitonic mechanism for high temperature superconductivity in YBa2Cu3O7

A. P. B. Sinha, P. V. Panat, R. E. Amritkar and K. P. Sinha, Phase Transitions 10, 203–212 (1987).

- Stochastic dynamical model for stock-stock correlations,

M. J. Ma, C. K. Hu and R. E. Amritkar, Phys. Rev. E 70, 026101–1-9 (2004).

# Fellowship / Member Of Academic Bodies

- Senior Associate - International Centre of Theoretical Physics, Trieste, Italy. 2001 to 2009

- Associate Member - International Centre of Theoretical Physics, Trieste, Italy. 1990 to 1998

- Fellow - Maharashtra Academy of Sciences

- Fellow - The National Academy of Sciences (Allahabad)

- Fellow - Indian Academy of Sciences (Bangalore)